The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation

Chunyan Liu; Chunyan Liu

doi:10.3934/math.20241619

AIMS Mathematics

2024, Volume 9, Issue 12: 33956-33972. doi: 10.3934/math.20241619

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Research article

The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation

Chunyan Liu ^,

College of Computer Science, Chengdu University, Chengdu 610106, China

Received: 31 July 2024 Revised: 10 November 2024 Accepted: 26 November 2024 Published: 02 December 2024
MSC : 34L30, 35B20, 35C05, 35C07

This article studies the phase portraits, chaotic patterns, and traveling wave solutions of the fractional order generalized Pochhammer–Chree equation. First, the fractional order generalized Pochhammer–Chree equation is transformed into an ordinary differential equation. Second, the dynamic behavior is analyzed using the planar dynamical system, and some three-dimensional and two-dimensional phase portraits are drawn using Maple software to reflect its chaotic behaviors. Finally, many solutions were constructed using the polynomial complete discriminant system method, including rational, trigonometric, hyperbolic, Jacobian elliptic function, and implicit function solutions. Two-dimensional graphics, three-dimensional graphics, and contour plots of some solutions are drawn.
- traveling wave solution,
- dynamics analysis,
- fractional,
- Pochhammer–Chree equation
Citation: Chunyan Liu. The traveling wave solution and dynamics analysis of the fractional order generalized Pochhammer–Chree equation[J]. AIMS Mathematics, 2024, 9(12): 33956-33972. doi: 10.3934/math.20241619

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Abstract

This article studies the phase portraits, chaotic patterns, and traveling wave solutions of the fractional order generalized Pochhammer–Chree equation. First, the fractional order generalized Pochhammer–Chree equation is transformed into an ordinary differential equation. Second, the dynamic behavior is analyzed using the planar dynamical system, and some three-dimensional and two-dimensional phase portraits are drawn using Maple software to reflect its chaotic behaviors. Finally, many solutions were constructed using the polynomial complete discriminant system method, including rational, trigonometric, hyperbolic, Jacobian elliptic function, and implicit function solutions. Two-dimensional graphics, three-dimensional graphics, and contour plots of some solutions are drawn.

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