EXACT SOLUTIONS AND BIFURCATION OF A MODIFIED GENERALIZED MULTIDIMENSIONAL FRACTIONAL KADOMTSEV–PETVIASHVILI EQUATION

Minyuan Liu, Hui Xu, Zenggui Wang and Guiying Chen
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Minyuan Liu: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Hui Xu: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Zenggui Wang: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Guiying Chen: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 03, 1-16

Abstract: In this paper, we investigate the exact solutions of a modified generalized multidimensional fractional Kadomtsev–Petviashvili (KP) equation by the bifurcation method. First, the equation is converted into a planar dynamical system through fractional complex wave transformation. The phase portraits of the equation and qualitative analysis are presented under different bifurcation conditions. Then, the bounded and unbounded traveling wave solutions, including periodic, kink, anti-kink, dark-solitary, bright-solitary and breaking wave solutions, are acquired by integrating along different orbits. Finally, numerical simulations of the dynamic behaviors of the solutions obtained are graphically illustrated by choosing appropriate parameters.

Keywords: Modified Generalized Multidimensional Fractional KP Equation; Bifurcation; Phase Portrait; Exact Solution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500464

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