EXACT SOLUTIONS AND BIFURCATION ANALYSIS OF THE TIME-FRACTIONAL EXTENDED (3 + 1)-DIMENSIONAL KADOMTSEV–PETVIASHVILI EQUATION WITH CONFORMABLE DERIVATIVE

Jing Zhang, Hui Meng, Zhen Zheng and Zenggui Wang
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Jing Zhang: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Hui Meng: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Zhen Zheng: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China
Zenggui Wang: School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 05, 1-28

Abstract: Exact traveling wave solutions of the conformable fractional extended (3 + 1)-dimensional Kadomtsev–Petviashvili equation are constructed. We apply four methods including the modified extended tanh-function method, the improved (G′/G) method, the two variables (G′/G, 1/G)-expansion method and the extended generalized Riccati equation mapping method. These methods are all expanded around Riccati equation, but each has unique advantages. Then various forms of solutions, such as breaking wave solutions, periodic solutions and soliton solutions can be obtained. Furthermore, the bifurcation analysis of this equation is also conducted. Dynamical features of the solutions by taking different values for parameters are illustrated by the 3D and 2D plots. Finally, we conduct discussions and comparisons of the results.

Keywords: Wave Equation; Fractional Derivative; Riccati Equation; Exact Solutions; Bifurcation Analysis (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500379

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