Qualitative analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative

Shan Zhao; Jun Feng; Shan Zhao; Jun Feng

doi:10.3934/era.2025165

Electronic Research Archive

2025, Volume 33, Issue 6: 3716-3732. doi: 10.3934/era.2025165

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Qualitative analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative

Shan Zhao ^{1,2
,
,},
Jun Feng ²

1.
School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu 610106, China
2.
Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059, China

Received: 06 March 2025 Revised: 09 May 2025 Accepted: 05 June 2025 Published: 13 June 2025

This study aims to investigate the qualitative behavior analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative. The equation serves as a prominent physics-based mathematical model with numerous practical uses. To analyze the studied equation, we convert it into an ordinary differential equation via traveling wave transformation and then apply the polynomial trial method to deduce its trial equation. Subsequently, the equation with periodically excited perturbation is analyzed using phase trajectory diagrams, bifurcation diagrams, and Lyapunov exponents. Additionally, by utilizing a polynomial complete discrimination system, we derive trigonometric, hyperbolic, and Jacobi elliptic function solutions, some of which are visually represented through figures. These findings enhance the theoretical understanding of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative and contribute to the study of nonlinear wave phenomena.
- nonlinear partial differential equation,
- trial equation method,
- polynomial complete discrimination system,
- Lyapunov exponent
Citation: Shan Zhao, Jun Feng. Qualitative analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative[J]. Electronic Research Archive, 2025, 33(6): 3716-3732. doi: 10.3934/era.2025165

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Abstract

This study aims to investigate the qualitative behavior analysis and traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative. The equation serves as a prominent physics-based mathematical model with numerous practical uses. To analyze the studied equation, we convert it into an ordinary differential equation via traveling wave transformation and then apply the polynomial trial method to deduce its trial equation. Subsequently, the equation with periodically excited perturbation is analyzed using phase trajectory diagrams, bifurcation diagrams, and Lyapunov exponents. Additionally, by utilizing a polynomial complete discrimination system, we derive trigonometric, hyperbolic, and Jacobi elliptic function solutions, some of which are visually represented through figures. These findings enhance the theoretical understanding of the (3+1)-dimensional Kadomtsev-Petviashvili-Sawada-Kotera-Ramani equation with conformable fractional derivative and contribute to the study of nonlinear wave phenomena.

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