The impact of standard Wiener process on the qualitative analysis and traveling wave solutions of stochastic nonlinear Kodama equation in the Stratonovich sense

Jin Wang; Zhao Li; Jin Wang; Zhao Li

doi:10.3934/math.20251107

AIMS Mathematics

2025, Volume 10, Issue 10: 24997-25010. doi: 10.3934/math.20251107

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Research article

The impact of standard Wiener process on the qualitative analysis and traveling wave solutions of stochastic nonlinear Kodama equation in the Stratonovich sense

Jin Wang ,
Zhao Li ^,

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

Received: 17 September 2025 Revised: 25 October 2025 Accepted: 28 October 2025 Published: 31 October 2025
MSC : 34H20, 35B20, 35C05, 35C07

This article investigates the qualitative analysis and traveling wave solutions of the stochastic nonlinear Kodama equation within the Stratonovich framework. By applying a random traveling wave transformation, the equation is first converted into an ordinary differential equation. The qualitative behavior of the corresponding two-dimensional dynamical system and its perturbation is then examined using planar dynamical system analysis. Subsequently, the complete discriminant system method is employed to derive four distinct types of optical solutions. Three-dimensional plots illustrating these solutions under different parameters are also presented.
- nonlinear Kodama equation,
- traveling wave solution,
- traveling wave transformation,
- stochastic,
- planar dynamical system
Citation: Jin Wang, Zhao Li. The impact of standard Wiener process on the qualitative analysis and traveling wave solutions of stochastic nonlinear Kodama equation in the Stratonovich sense[J]. AIMS Mathematics, 2025, 10(10): 24997-25010. doi: 10.3934/math.20251107

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Abstract

This article investigates the qualitative analysis and traveling wave solutions of the stochastic nonlinear Kodama equation within the Stratonovich framework. By applying a random traveling wave transformation, the equation is first converted into an ordinary differential equation. The qualitative behavior of the corresponding two-dimensional dynamical system and its perturbation is then examined using planar dynamical system analysis. Subsequently, the complete discriminant system method is employed to derive four distinct types of optical solutions. Three-dimensional plots illustrating these solutions under different parameters are also presented.

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