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ORIGINAL RESEARCH article
Front. Phys.
Sec. Statistical and Computational Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1502570
This article is part of the Research Topic Advances in Nonperturbative Approaches: Methods, Algorithms, and Applications View all 3 articles
Bifurcation, chaotic behavior and traveling wave solutions of the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation
Provisionally accepted- Chengdu University, Chengdu, China
The space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM)equation is a significant nonlinear model equation to illustrate numerous physical structures suchas water wave mechanics, fluid flow, marine and coastal science, control system and so on. In thisarticle, the dynamical behavior of the space-time fractional ZKBBM equation is analyzed and itstraveling wave solutions are investigated based on the theory of the cubic polynomial complete dis-criminant system. First, the equation is transformed into a nonlinear ordinary differential equationthrough the complex wave transformation. Then the dynamical behavior analysis of the equationare discussed in accordance with the bifurcation theory of planar dynamical system indicates. Afterthat, by utilizing the polynomial complete discriminant system and root formulas, several new exacttraveling wave solutions of the equation are obtained. At the last, the plots of some solutions areshown with the aid of MATLAB software in order to exhibit the structure of the solutions.
Keywords: nonlinear fractional partial differential equation, bifurcation theory, dynamic analysis, Planar dynamical system, Polynomial complete discriminant system
Received: 27 Sep 2024; Accepted: 31 Mar 2025.
Copyright: © 2025 Zhao and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Shan Zhao, Chengdu University, Chengdu, China
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