Searching for traveling wave solutions of nonlinear evolution equations in mathematical physics

In this article, meromorphic exact solutions for the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (gCBS) equation are obtained by using the complex method. With the applications of our results, traveling wave exact solutions of the breaking soliton equation are achieved. The dynamic behaviors of exact solutions of the (2 + 1)-dimensional gCBS equation are shown by some graphs. In particular, the graphs of elliptic function solutions are comparatively rare in other literature. The idea of this study can be applied to the complex nonlinear systems of some areas of engineering.

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“…The (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff (gCBS) equation [39] is the potential form of Eq. (1.1) that is given as:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Aminakbari

Yuan

2020

Open Mathematics

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“…One of the main functions for finding symmetry reductions is to use them to seek exact solutions. There are many effective direct methods that can be used to solve the obtained reduced equations such as the tanh method [28], the homogeneous balance method [29], the Horota bilinear method [30], the Darboux transformation method [31], and so on (see [32][33][34][35][36][37][38][39] for reference). Here, we use the traveling wave transformation to transform reduced equations (11) and (12) to ODEs for obtaining exact solutions.…”

Section: Discussion Of the Solutions Of Mzk Equationmentioning

confidence: 99%

Symmetry reductions of the ( 3 + 1 ) $(3+1)$ -dimensional modified Zakharov–Kuznetsov equation

et al. 2019

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This paper is concerned with the symmetry reductions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. The direct symmetry method is applied to determine the symmetry and the corresponding vector field. Then, the considered equation is reduced to lower-dimensional equations with the aid of the obtained symmetry. At last, some exact solutions of the modified Zakharov-Kuznetsov equation are found in terms of the lower-dimensional equations.

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“…There are many excellent works on solving analytical solutions of partial differential equations (see [6,9]). For many kinds of subdiffusion equations, it is difficult to obtain their analytical solutions.…”

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confidence: 99%

On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations

Wei

Zhao

Chen

et al. 2022

Numerical Methods Partial

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This paper analyzes a class of two-dimensional (2-D) time fractional reaction-subdiffusion equations with variable coefficients. The high-order L2-1 𝜎 time-stepping scheme on graded meshes is presented to deal with the weak singularity at the initial time t = 0, and the bilinear finite element method (FEM) on anisotropic meshes is used for spatial discretization. Using the modified discrete fractional Grönwall inequality, and combining the interpolation operator and the projection operator, the L 2 -norm error estimation and H 1 -norm superclose results are rigorously proved. The superconvergence result in the H 1 -norm is derived by applying the interpolation postprocessing technique. Finally, numerical examples are presented to verify the validation of our theoretical analysis.

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Searching for traveling wave solutions of nonlinear evolution equations in mathematical physics

Cited by 4 publications

References 25 publications

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Symmetry reductions of the ( 3 + 1 ) $(3+1)$ -dimensional modified Zakharov–Kuznetsov equation

On the convergence and superconvergence for a class of two‐dimensional time fractional reaction‐subdiffusion equations

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