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Solitary wave solution and a linear mass-conservative difference scheme for the generalized Korteweg–de Vries–Kawahara equation

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Abstract

In this work, an exact solitary wave solution and a linear conservative difference scheme for solving the generalized Korteweg–de Vries–Kawahara (GKdV-K) equation are proposed. We first use the Ansatz’s method to derive the exact solitary wave solution for the GKdV-K equation and then develop a three-level linear conservative finite difference scheme for solving the equation. The mass conservation, solvability, stability and convergence of the numerical solution are rigorously proved. The scheme is second-order accurate in both time and space variables. We further extend the numerical method and theoretical analysis to the 2D GKdV-K equation. Comparisons between the solutions obtained from the exact solitary wave solution and the linear finite difference scheme are made to demonstrate that the present scheme is efficient and reliable.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable suggestions which improve the quality of the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, 363000, Fujian, People’s Republic of China

    Xiaofeng Wang & Hong Cheng

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  1. Xiaofeng Wang
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  2. Hong Cheng
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Correspondence to Xiaofeng Wang.

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Communicated by Hui Liang.

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The authors are supported by the Natural Science Foundation of Fujian Province, China (No: 2020J01796).

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Wang, X., Cheng, H. Solitary wave solution and a linear mass-conservative difference scheme for the generalized Korteweg–de Vries–Kawahara equation. Comp. Appl. Math. 40, 273 (2021). https://doi.org/10.1007/s40314-021-01668-3

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  • DOI: https://doi.org/10.1007/s40314-021-01668-3

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