The improved sub-equation method is employed to construct exact solutions of (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation. By studying the dynamical behavior and exact solutions of the sub-equation, we obtain more types of exact solutions such as analytical bright and dark solitons, analytical kink or anti-kink solitons, analytical and singular periodic waves. In addition, some selected solutions are visualized through 2D and 3D simulations in order to obtain the best physical characterization of the obtained results. This method is very effective and can be used to study other nonlinear problems.

improved sub-equation method, mKdV-ZK equation, bifurcation, soliton solution, periodic solution.

Received: December 14, 2023;  Accepted: February 2, 2024; Published: March 6, 2024

How to cite this article: Dahe Feng, Jibin Li and Jianjun Jiao, Analytical and singular exact solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation, Far East Journal of Applied Mathematics 117(1) (2024), 19-47. http://dx.doi.org/10.17654/0972096024002

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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