Exact traveling wave solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli system using (G′G2) expansion method

Devi, Preeti; Singh, Kajal

doi:10.1063/5.0003694

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…The travelling waves solutions of biological population model of fractional order, the Burgers equation with time-fractional order, and the space-time fractional Whitham-Broer-Kaup model were investigated by Arshed and Sadia [30] by using the (G /G 2 )-expansion methodology in 2018. In 2020, the (G /G 2 )-expansion method was used to build numerous novel accurate travelling wave solutions for the Boiti-Leon-Pempinelli system in two dimensions [31]. The unidirectional Dullin-Gottwald-Holm (DGH) system describing wave prorogation in shallow water, which include singular periodic wave solutions, shock-singular, shock, and singular solutions investigated in 2021 by Bilal et al [32] to find novel exact solutions via the (G /G 2 )-expansion approach.…”

Section: Introductionmentioning

confidence: 99%

Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations

Shakeel

Chung

2022

Fractal Fract

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In this article, a new method for obtaining closed-form solutions of the simplified modified Camassa-Holm (MCH) equation, a nonlinear fractional partial differential equation, is suggested. The modified Riemann-Liouville fractional derivative and the wave transformation are used to convert the fractional order partial differential equation into an integer order ordinary differential equation. Using the novel (G’/G2)-expansion method, several exact solutions with extra free parameters are found in the form of hyperbolic, trigonometric, and rational function solutions. When parameters are given appropriate values along with distinct values of fractional order α travelling wave solutions such as singular periodic waves, singular kink wave soliton solutions are formed which are forms of soliton solutions. Also, the solutions obtained by the proposed method depend on the value of the arbitrary parameters H. Previous results are re-derived when parameters are given special values. Furthermore, for numerical presentations in the form of 3D and 2D graphics, the commercial software Mathematica 10 is incorporated. The method is accurately depicted, and it provides extra general exact solutions.

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Section: Introductionmentioning

confidence: 99%

Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations

Shakeel

Chung

2022

Fractal Fract

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“…In the past couple of decades, many robust, efficient, and powerful methods exist that have been developed for finding exact solutions of NLEEs, including the (G /G, 1/G)-expansion method [11], the enhanced (G /G)-expansion method [12], the exp-function method [13], the Jacobi elliptic equation method [14], the generalized Kudryashov's method [15], the sine-Gordon expansion method [16], the sub-equation method [17], the improved tan(φ/2)-expansion method [18], and the extended direct algebraic method [19,20]. More recently, the (G /G 2 )-expansion method [4,[21][22][23][24][25][26][27][28][29] has attracted a remarkable amount of attention of many researchers who employed the method to construct exact solutions of certain NPDEs. In 2018, Arshed and Sadia [23] used the (G /G 2 )-expansion method to obtain some new traveling wave solutions for the time-fractional Burgers equation, the fractional biological population model, and the space-time fractional Whitham-Broer-Kaup equations.…”

Section: Introductionmentioning

confidence: 99%

“…Sirisubtawee and Koonprasert [24] utilized the method to solve the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system for their exact solutions including trigonometric, exponential, and rational function solutions. In 2020, the (G /G 2 )-expansion approach was employed to construct some novel exact traveling wave solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system [28]. In 2021, Bilal et al [29] proposed new exact solutions, which consist of shock, singular, shock-singular, and singular periodic wave solutions obtained by the (G /G 2 )expansion method, to unidirectional Dullin-Gottwald-Holm (DGH) system describing the prorogation of waves in shallow water.…”

Section: Introductionmentioning

confidence: 99%

Applications of the (G′/G2)-Expansion Method for Solving Certain Nonlinear Conformable Evolution Equations

et al. 2021

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The core objective of this article is to generate novel exact traveling wave solutions of two nonlinear conformable evolution equations, namely, the (2+1)-dimensional conformable time integro-differential Sawada–Kotera (SK) equation and the (3+1)-dimensional conformable time modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation using the (G′/G2)-expansion method. These two equations associate with conformable partial derivatives with respect to time which the former equation is firstly proposed in the form of the conformable integro-differential equation. To the best of the authors’ knowledge, the two equations have not been solved by means of the (G′/G2)-expansion method for their exact solutions. As a result, some exact solutions of the equations expressed in terms of trigonometric, exponential, and rational function solutions are reported here for the first time. Furthermore, graphical representations of some selected solutions, plotted using some specific sets of the parameter values and the fractional orders, reveal certain physical features such as a singular single-soliton solution and a doubly periodic wave solution. These kinds of the solutions are usually discovered in natural phenomena. In particular, the soliton solution, which is a solitary wave whose amplitude, velocity, and shape are conserved after a collision with another soliton for a nondissipative system, arises ubiquitously in fluid mechanics, fiber optics, atomic physics, water waves, and plasmas. The method, along with the help of symbolic software packages, can be efficiently and simply used to solve the proposed problems for trustworthy and accurate exact solutions. Consequently, the method could be employed to determine some new exact solutions for other nonlinear conformable evolution equations.

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Classical symmetries of the Klein–Gordon–Zakharov equations with time-dependent variable coefficients

Devi,

Guleria

2024

Arab. J. Math.

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In this article, we employ the group-theoretic methods to explore the Lie symmetries of the Klein–Gordon–Zakharov equations, which include time-dependent coefficients. We obtain the Lie point symmetries admitted by the Klein–Gordon–Zakharov equations along with the forms of variable coefficients. From the resulting symmetries, we construct similarity reductions.The similarity reductions are further analyzed using the power series method/approach and furnished the series solutions. Additionally, the convergence of the series solutions has been reported.

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Exact traveling wave solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli system using (G′G2) expansion method

Cited by 4 publications

References 26 publications

Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations

Novel Analytical Technique to Find Closed Form Solutions of Time Fractional Partial Differential Equations

Applications of the (G′/G2)-Expansion Method for Solving Certain Nonlinear Conformable Evolution Equations

Classical symmetries of the Klein–Gordon–Zakharov equations with time-dependent variable coefficients

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