## What is/are Direct Algebraic?

Direct Algebraic - The integration mechanism that was adopted is modified direct algebraic method, which extracts different solitons (dark and singular) and combo (dark-singular) solitons for different values of parameters.^{[1]}This paper can be considered as a generalization of [9], where instead of reconstructing point-wise dislocations, as done in the latter paper, our aim is to recover the parameters of line dislocations by employing a direct algebraic algorithm.

^{[2]}In this article, the modified direct algebraic method is applied for the perturbed nonlinear Schrodinger equation (NLSE) describing the dynamics of optical solitons in metamaterials, in the presence of quadratic-cubic nonlinearity.

^{[3]}For unperturbed model a variety of solitonic structures are calculated using a direct algebraic method.

^{[4]}Fractional Fokas equation is studied, its exact solution is obtained by the direct algebraic method.

^{[5]}This paper suggests a direct algebraic method for finding exact solutions of the space-time fractional (2+1)-dimensional breaking soliton equation.

^{[6]}In this present work, we retrieve a series of soliton solutions to the coupled nonlinear Schrodinger type equations by applying an integration gadget known as the new extended direct algebraic method.

^{[7]}A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method.

^{[8]}A variety of nonlinear dynamical optical soliton structures are extracted in different shapes like hyperbolic, trigonometric, and plan wave solutions including some specifically known solitary wave solutions like bright, dark, singular, and combo solitons by engaging three efficient mathematical tools namely the extended sinh-Gordon equation expansion metho, ( $$\frac{G^{\prime }}{G^2}$$ G ′ G 2 )-expansion function method and the modified direct algebraic method).

^{[9]}A novel method is presented which is called the new extended direct algebraic method (EDAM).

^{[10]}In this paper direct algebraic method applied for the coupled Higgs equation.

^{[11]}Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus.

^{[12]}The analytical and numerical solutions of the (2+1) dimensional, Fisher-Kolmogorov-Petrovskii-Piskunov ((2+1) D-Fisher-KPP) model are investigated by employing the modified direct algebraic (MDA), modified Kudryashov (MKud.

^{[13]}In this work, we obtain different soliton solutions to coupled nonlinear Schrödinger-type (CNLST) equations by applying three integration tools known as the G′G2 -expansion function method, the modified direct algebraic method (MDAM), and the generalized Kudryashov method.

^{[14]}This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs).

^{[15]}The modified extended direct algebraic method is applied to obtain many new exact travel wave solutions in magneto-optic waveguides which keep triple power law nonlinearity.

^{[16]}In this paper, the new general extended direct algebraic method is applied to achieve optical solitons of Biswas-Arshed equation with birefringent fiber involving two component vector soliton.

^{[17]}A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials.

^{[18]}For this sake modified extended direct algebraic (MEDA) and ( G ′ / G ) -expansion techniques are used.

^{[19]}For electron acoustic solitary waves (EASWs), using the new extended direct algebraic approach, soliton solutions have also documented.

^{[20]}In this research work, we retrieve dynamics of new soliton solutions to the Kraenkel-Manna-Merle system which describes the nonlinear ultrashort pulse in saturated ferromagnetic materials having an external field with zero-conductivity by utilizing the new extended direct algebraic method.

^{[21]}The direct algebraic method, together with the inheritance solving strategy, is utilized to construct multiwave interaction solutions among solitons, rational waves and periodic waves for a (3+1)-d.

^{[22]}Manuscript purpose is to find analytical solutions of the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chain and Vakhnenko dynamical equations by using the generalized direct algebraic and simple equation analytical methods.

^{[23]}The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions.

^{[24]}Different kinds of solutions such as hyperbolic, trigonometric, Jacobi elliptic, and rational function including some special known solitary waves like shock, singular, combo shock-solitary wave, and multiple soliton solutions are achieved by the utilization of the sound computational integration tools namely the new Φ 6 -model expansion method and modified direct algebraic method (MDAM).

^{[25]}The new extended direct algebraic method (NEDAM) is a viable and successful mathematical method to construct the traveling wave patterns of science and engineering problems.

^{[26]}The new modified extended direct algebraic (MEDA) approach is adopted to investigate the diverse nonlinear wave structures.

^{[27]}We have used new Direct Algebraic method to calculate solitonic structures.

^{[28]}In this article, we describe several enhancements of a three-phase correlation image sensor (3PCIS) toward its uses for a direct algebraic method of optical flow detection, i.

^{[29]}The worked out new analytical system solution provides easy- and fast-to-use explicit formulas (for direct algebraic substitutions) to determine both the temperature of the collector and the temperature of the storage.

^{[30]}In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique.

^{[31]}In this paper, we applied the extended direct algebraic method (EDAM) to examine the dark, singular, combined dark-bright, combined bright-singular and periodic singular solitons as well as hyperbolic and trigonometric functions solutions of Biswas-Arshed equation (BAE) in birefringent fibers.

^{[32]}The findings in this study are two ways that prospective teachers use area measurements (geometric representations) to solve algebraic problems, namely direct algebraic-geometric translation and algebraic-geometric translations based on the results of factorization.

^{[33]}A new extended direct algebraic equation method was successfully applied to extract the solitons solutions.

^{[34]}We develop new solutions of complex hyperbolic Schrodinger’s model using a method that is the latest extended direct algebraic method.

^{[35]}To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill.

^{[36]}In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method).

^{[37]}We bypass technically challenging direct algebraic computations with a novel technique that relies on an auxiliary function, which is related to the Higgs potential but which is easier to analyze.

^{[38]}However, by employing the new extended direct algebraic method and the improved Sub-ODE equation, we recovered W-shape bright soliton, dark soliton, periodic solutions, rational solutions and Weierstrass elliptic function solutions.

^{[39]}For the unperturbed considered model diverse solitonic structures are measured using two finest approaches which are extended ( G ′ G 2 ) -expansion method and the direct algebraic method.

^{[40]}Investigating solitons structures of such an equation, we make use for the purpose, of a mathematical tool which is a new generalized extended direct algebraic method (NGEDAM).

^{[41]}Using the modified auxiliary equation of direct algebraic method, we study the considered nonlinear PDEs analytically.

^{[42]}In this paper, we investigate miscellaneous new traveling wave solutions of the generalized nonlinear Schrodinger equation modeling few-cycle pulse propagation in metamaterials by the new extended direct algebraic method.

^{[43]}Meanwhile, rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method.

^{[44]}In the present paper, we use a direct algebraic method that also yields all rational solutions, albeit parameterized in a way very different from that obtained by Barnett (and Hajja), and we establish an explicit, nonobvious, birational correspondence between the two parameterizations.

^{[45]}But this is not the direct algebraic deduction of the corresponding energies.

^{[46]}In this paper, the extended direct algebraic method is applied to investigate the complex trigonometric and hyperbolic function solutions, especially dark, singular, combined dark-bright, combined singular, combined dark-singular, combined bright-singular solitons and periodic-singular solutions are obtained of the conformable space-time fractional Fokas–Lenells equation.

^{[47]}We use two different approaches: a classical gradient descent and a direct algebraic method that is based on a complex-valued encoding of the spikes.

^{[48]}In this paper, with the aid of the Maple software, the new extended direct algebraic method is used as a powerful method to constructs some new solutions to the well-known nonlinear models, namely, the simplified modified Camassa-Holm equation.

^{[49]}This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled $$(2+1)$$(2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation.

^{[50]}

## expansion function method

A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method.^{[1]}A variety of nonlinear dynamical optical soliton structures are extracted in different shapes like hyperbolic, trigonometric, and plan wave solutions including some specifically known solitary wave solutions like bright, dark, singular, and combo solitons by engaging three efficient mathematical tools namely the extended sinh-Gordon equation expansion metho, ( $$\frac{G^{\prime }}{G^2}$$ G ′ G 2 )-expansion function method and the modified direct algebraic method).

^{[2]}In this work, we obtain different soliton solutions to coupled nonlinear Schrödinger-type (CNLST) equations by applying three integration tools known as the G′G2 -expansion function method, the modified direct algebraic method (MDAM), and the generalized Kudryashov method.

^{[3]}

## interaction solutions among

The direct algebraic method, together with the inheritance solving strategy, is utilized to construct multiwave interaction solutions among solitons, rational waves and periodic waves for a (3+1)-d.^{[1]}To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill.

^{[2]}

## 2 + 1

Manuscript purpose is to find analytical solutions of the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chain and Vakhnenko dynamical equations by using the generalized direct algebraic and simple equation analytical methods.^{[1]}In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method).

^{[2]}

## + 1 dimensional

In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique.^{[1]}

## Extended Direct Algebraic

In this present work, we retrieve a series of soliton solutions to the coupled nonlinear Schrodinger type equations by applying an integration gadget known as the new extended direct algebraic method.^{[1]}A novel method is presented which is called the new extended direct algebraic method (EDAM).

^{[2]}The modified extended direct algebraic method is applied to obtain many new exact travel wave solutions in magneto-optic waveguides which keep triple power law nonlinearity.

^{[3]}In this paper, the new general extended direct algebraic method is applied to achieve optical solitons of Biswas-Arshed equation with birefringent fiber involving two component vector soliton.

^{[4]}A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials.

^{[5]}For this sake modified extended direct algebraic (MEDA) and ( G ′ / G ) -expansion techniques are used.

^{[6]}For electron acoustic solitary waves (EASWs), using the new extended direct algebraic approach, soliton solutions have also documented.

^{[7]}In this research work, we retrieve dynamics of new soliton solutions to the Kraenkel-Manna-Merle system which describes the nonlinear ultrashort pulse in saturated ferromagnetic materials having an external field with zero-conductivity by utilizing the new extended direct algebraic method.

^{[8]}The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions.

^{[9]}The new extended direct algebraic method (NEDAM) is a viable and successful mathematical method to construct the traveling wave patterns of science and engineering problems.

^{[10]}The new modified extended direct algebraic (MEDA) approach is adopted to investigate the diverse nonlinear wave structures.

^{[11]}In this paper, we applied the extended direct algebraic method (EDAM) to examine the dark, singular, combined dark-bright, combined bright-singular and periodic singular solitons as well as hyperbolic and trigonometric functions solutions of Biswas-Arshed equation (BAE) in birefringent fibers.

^{[12]}A new extended direct algebraic equation method was successfully applied to extract the solitons solutions.

^{[13]}We develop new solutions of complex hyperbolic Schrodinger’s model using a method that is the latest extended direct algebraic method.

^{[14]}However, by employing the new extended direct algebraic method and the improved Sub-ODE equation, we recovered W-shape bright soliton, dark soliton, periodic solutions, rational solutions and Weierstrass elliptic function solutions.

^{[15]}Investigating solitons structures of such an equation, we make use for the purpose, of a mathematical tool which is a new generalized extended direct algebraic method (NGEDAM).

^{[16]}In this paper, we investigate miscellaneous new traveling wave solutions of the generalized nonlinear Schrodinger equation modeling few-cycle pulse propagation in metamaterials by the new extended direct algebraic method.

^{[17]}In this paper, the extended direct algebraic method is applied to investigate the complex trigonometric and hyperbolic function solutions, especially dark, singular, combined dark-bright, combined singular, combined dark-singular, combined bright-singular solitons and periodic-singular solutions are obtained of the conformable space-time fractional Fokas–Lenells equation.

^{[18]}In this paper, with the aid of the Maple software, the new extended direct algebraic method is used as a powerful method to constructs some new solutions to the well-known nonlinear models, namely, the simplified modified Camassa-Holm equation.

^{[19]}This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled $$(2+1)$$(2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation.

^{[20]}In this paper, the practice of the extended direct algebraic method (EDAM) is used to solve fractional Regularized Long Wave Burgers (RLW-Burgers) equation by means of the conformable derivative.

^{[21]}Also, the study reviewed the superiority of the method compared to extended direct algebraic method, extended direct algebraic mapping and extended Sech-tanh methods.

^{[22]}In this paper, the process of the extended direct algebraic method (EDAM) is used to solve two fractional Boussinesq-like equations by means of conformable derivatives.

^{[23]}This paper employs modified extended direct algebraic method to recover bright, dark and singular solitons for resonant nonlinear Schrodinger's equation that is studied with dual-power law media.

^{[24]}In this paper and for the first time, we describe and introduce a new extended direct algebraic method which is a new method for solving nonlinear partial differential equations arising in nonlinear optics and nonlinear science.

^{[25]}This article deal with finding travelling wave solutions for the seventh order Sawada-Kotera Ito dynamiclal wave equation which describes the evolution of steeper waves of shorter wavelength than KdV equations using modified extended direct algebraic method.

^{[26]}This paper investigates the soliton solutions of Kundu–Eckhaus equation for birefringent fibers, by employing two resourceful integration techniques, which are extended (G′/G)-expansion method and extended direct algebraic method.

^{[27]}In this study, several novel solutions of strain wave equation for micro-structured solids are obtained by using the powerful modified extended direct algebraic method.

^{[28]}The Q − function method and extended direct algebraic method are applied.

^{[29]}ABSTRACT In this study, the dynamical analysis of optical dark and singular solitons is carried out for chiral (1+2)-dimensional nonlinear Schrödinger’s equation with the implementation of extended direct algebraic and extended trial equation method independently.

^{[30]}

## Modified Direct Algebraic

The integration mechanism that was adopted is modified direct algebraic method, which extracts different solitons (dark and singular) and combo (dark-singular) solitons for different values of parameters.^{[1]}In this article, the modified direct algebraic method is applied for the perturbed nonlinear Schrodinger equation (NLSE) describing the dynamics of optical solitons in metamaterials, in the presence of quadratic-cubic nonlinearity.

^{[2]}A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method.

^{[3]}A variety of nonlinear dynamical optical soliton structures are extracted in different shapes like hyperbolic, trigonometric, and plan wave solutions including some specifically known solitary wave solutions like bright, dark, singular, and combo solitons by engaging three efficient mathematical tools namely the extended sinh-Gordon equation expansion metho, ( $$\frac{G^{\prime }}{G^2}$$ G ′ G 2 )-expansion function method and the modified direct algebraic method).

^{[4]}The analytical and numerical solutions of the (2+1) dimensional, Fisher-Kolmogorov-Petrovskii-Piskunov ((2+1) D-Fisher-KPP) model are investigated by employing the modified direct algebraic (MDA), modified Kudryashov (MKud.

^{[5]}In this work, we obtain different soliton solutions to coupled nonlinear Schrödinger-type (CNLST) equations by applying three integration tools known as the G′G2 -expansion function method, the modified direct algebraic method (MDAM), and the generalized Kudryashov method.

^{[6]}Different kinds of solutions such as hyperbolic, trigonometric, Jacobi elliptic, and rational function including some special known solitary waves like shock, singular, combo shock-solitary wave, and multiple soliton solutions are achieved by the utilization of the sound computational integration tools namely the new Φ 6 -model expansion method and modified direct algebraic method (MDAM).

^{[7]}In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method).

^{[8]}

## Generalized Direct Algebraic

Manuscript purpose is to find analytical solutions of the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chain and Vakhnenko dynamical equations by using the generalized direct algebraic and simple equation analytical methods.^{[1]}In our research, we ascertain abundant novel exact traveling wave solutions of (2 + 1)-dimensional first integro-differential Kadomtsev-Petviashivili hierarchy equation by two new modified mathematical methods namely called generalized direct algebraic and extended simple equation methods with the help of computer package like Mathematica.

^{[2]}

## direct algebraic method

The integration mechanism that was adopted is modified direct algebraic method, which extracts different solitons (dark and singular) and combo (dark-singular) solitons for different values of parameters.^{[1]}In this article, the modified direct algebraic method is applied for the perturbed nonlinear Schrodinger equation (NLSE) describing the dynamics of optical solitons in metamaterials, in the presence of quadratic-cubic nonlinearity.

^{[2]}For unperturbed model a variety of solitonic structures are calculated using a direct algebraic method.

^{[3]}Fractional Fokas equation is studied, its exact solution is obtained by the direct algebraic method.

^{[4]}This paper suggests a direct algebraic method for finding exact solutions of the space-time fractional (2+1)-dimensional breaking soliton equation.

^{[5]}In this present work, we retrieve a series of soliton solutions to the coupled nonlinear Schrodinger type equations by applying an integration gadget known as the new extended direct algebraic method.

^{[6]}A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method.

^{[7]}A variety of nonlinear dynamical optical soliton structures are extracted in different shapes like hyperbolic, trigonometric, and plan wave solutions including some specifically known solitary wave solutions like bright, dark, singular, and combo solitons by engaging three efficient mathematical tools namely the extended sinh-Gordon equation expansion metho, ( $$\frac{G^{\prime }}{G^2}$$ G ′ G 2 )-expansion function method and the modified direct algebraic method).

^{[8]}A novel method is presented which is called the new extended direct algebraic method (EDAM).

^{[9]}In this paper direct algebraic method applied for the coupled Higgs equation.

^{[10]}In this work, we obtain different soliton solutions to coupled nonlinear Schrödinger-type (CNLST) equations by applying three integration tools known as the G′G2 -expansion function method, the modified direct algebraic method (MDAM), and the generalized Kudryashov method.

^{[11]}The modified extended direct algebraic method is applied to obtain many new exact travel wave solutions in magneto-optic waveguides which keep triple power law nonlinearity.

^{[12]}In this paper, the new general extended direct algebraic method is applied to achieve optical solitons of Biswas-Arshed equation with birefringent fiber involving two component vector soliton.

^{[13]}A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials.

^{[14]}In this research work, we retrieve dynamics of new soliton solutions to the Kraenkel-Manna-Merle system which describes the nonlinear ultrashort pulse in saturated ferromagnetic materials having an external field with zero-conductivity by utilizing the new extended direct algebraic method.

^{[15]}The direct algebraic method, together with the inheritance solving strategy, is utilized to construct multiwave interaction solutions among solitons, rational waves and periodic waves for a (3+1)-d.

^{[16]}The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions.

^{[17]}Different kinds of solutions such as hyperbolic, trigonometric, Jacobi elliptic, and rational function including some special known solitary waves like shock, singular, combo shock-solitary wave, and multiple soliton solutions are achieved by the utilization of the sound computational integration tools namely the new Φ 6 -model expansion method and modified direct algebraic method (MDAM).

^{[18]}The new extended direct algebraic method (NEDAM) is a viable and successful mathematical method to construct the traveling wave patterns of science and engineering problems.

^{[19]}We have used new Direct Algebraic method to calculate solitonic structures.

^{[20]}In this article, we describe several enhancements of a three-phase correlation image sensor (3PCIS) toward its uses for a direct algebraic method of optical flow detection, i.

^{[21]}In this paper, a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation is investigated and its various new interaction solutions among solitons, rational waves and periodic waves are obtained by the direct algebraic method, together with the inheritance solving technique.

^{[22]}In this paper, we applied the extended direct algebraic method (EDAM) to examine the dark, singular, combined dark-bright, combined bright-singular and periodic singular solitons as well as hyperbolic and trigonometric functions solutions of Biswas-Arshed equation (BAE) in birefringent fibers.

^{[23]}We develop new solutions of complex hyperbolic Schrodinger’s model using a method that is the latest extended direct algebraic method.

^{[24]}To construct a class of new multiwave interaction solutions for the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, we calculate different types of interaction solutions among solitons, periodic waves and rational waves using the direct algebraic method together with the inheritance solving skill.

^{[25]}However, by employing the new extended direct algebraic method and the improved Sub-ODE equation, we recovered W-shape bright soliton, dark soliton, periodic solutions, rational solutions and Weierstrass elliptic function solutions.

^{[26]}For the unperturbed considered model diverse solitonic structures are measured using two finest approaches which are extended ( G ′ G 2 ) -expansion method and the direct algebraic method.

^{[27]}Investigating solitons structures of such an equation, we make use for the purpose, of a mathematical tool which is a new generalized extended direct algebraic method (NGEDAM).

^{[28]}Using the modified auxiliary equation of direct algebraic method, we study the considered nonlinear PDEs analytically.

^{[29]}In this paper, we investigate miscellaneous new traveling wave solutions of the generalized nonlinear Schrodinger equation modeling few-cycle pulse propagation in metamaterials by the new extended direct algebraic method.

^{[30]}Meanwhile, rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method.

^{[31]}In the present paper, we use a direct algebraic method that also yields all rational solutions, albeit parameterized in a way very different from that obtained by Barnett (and Hajja), and we establish an explicit, nonobvious, birational correspondence between the two parameterizations.

^{[32]}In this paper, the extended direct algebraic method is applied to investigate the complex trigonometric and hyperbolic function solutions, especially dark, singular, combined dark-bright, combined singular, combined dark-singular, combined bright-singular solitons and periodic-singular solutions are obtained of the conformable space-time fractional Fokas–Lenells equation.

^{[33]}We use two different approaches: a classical gradient descent and a direct algebraic method that is based on a complex-valued encoding of the spikes.

^{[34]}In this paper, with the aid of the Maple software, the new extended direct algebraic method is used as a powerful method to constructs some new solutions to the well-known nonlinear models, namely, the simplified modified Camassa-Holm equation.

^{[35]}This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled $$(2+1)$$(2+1)-dimensional Konopelchenko–Dubrovsky (KD) equation.

^{[36]}In this paper, the practice of the extended direct algebraic method (EDAM) is used to solve fractional Regularized Long Wave Burgers (RLW-Burgers) equation by means of the conformable derivative.

^{[37]}Also, the study reviewed the superiority of the method compared to extended direct algebraic method, extended direct algebraic mapping and extended Sech-tanh methods.

^{[38]}In this paper, the process of the extended direct algebraic method (EDAM) is used to solve two fractional Boussinesq-like equations by means of conformable derivatives.

^{[39]}This paper employs modified extended direct algebraic method to recover bright, dark and singular solitons for resonant nonlinear Schrodinger's equation that is studied with dual-power law media.

^{[40]}In this work, we use the extended form of two methods, auxiliary equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs.

^{[41]}In this paper and for the first time, we describe and introduce a new extended direct algebraic method which is a new method for solving nonlinear partial differential equations arising in nonlinear optics and nonlinear science.

^{[42]}This article deal with finding travelling wave solutions for the seventh order Sawada-Kotera Ito dynamiclal wave equation which describes the evolution of steeper waves of shorter wavelength than KdV equations using modified extended direct algebraic method.

^{[43]}This paper investigates the soliton solutions of Kundu–Eckhaus equation for birefringent fibers, by employing two resourceful integration techniques, which are extended (G′/G)-expansion method and extended direct algebraic method.

^{[44]}In this study, several novel solutions of strain wave equation for micro-structured solids are obtained by using the powerful modified extended direct algebraic method.

^{[45]}The Q − function method and extended direct algebraic method are applied.

^{[46]}