Qualitative analysis and new traveling wave solutions for the stochastic Biswas-Milovic equation

Dan Chen; Da Shi; Feng Chen; Dan Chen; Da Shi; Feng Chen

doi:10.3934/math.2025190

AIMS Mathematics

2025, Volume 10, Issue 2: 4092-4119. doi: 10.3934/math.2025190

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Research article

Qualitative analysis and new traveling wave solutions for the stochastic Biswas-Milovic equation

1.
College of Computer Science, Chengdu University, Chengdu 610106, China
2.
Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610068, China
3.
School of Mechanical Engineering, Chengdu University, Chengdu 610106, China

Received: 10 December 2024 Revised: 13 February 2025 Accepted: 20 February 2025 Published: 27 February 2025
MSC : 35B20, 35B32, 35C07, 60H15

In this paper, we investigated the planar dynamical system and new traveling wave solution of the stochastic Biswas-Milovic equation (BME) with dual-power law nonlinearity and multiplicative white noise in the Itô sense. First, the stochastic BME with dual-power law nonlinearity and multiplicative white noise in the Itô sense was transformed into a nonlinear ordinary differential equation (NLODE) through traveling wave transformation. Second, the dynamical bifurcation conditions and phase diagrams of the equation considered were obtained through the method of planar dynamical systems, and the phase portrait of the dynamical system was given. Moreover, taking into account the periodic disturbances in real-world environments, we extended our analysis to explore the effects of disturbance terms. Meanwhile, two-dimensional (2D) and three-dimensional (3D) phase portraits, sensitivity analyses, and the Poincaré section of its perturbed system were plotted through Maple software. Finally, the new traveling wave solutions of the stochastic BME with dual-power law nonlinearity and multiplicative white noise in the Itô sense were constructed by using the complete discrimination system method.
- stochastic Biswas-Milovic equation,
- planar dynamical system,
- traveling wave solutions,
- complete discrimination system
Citation: Dan Chen, Da Shi, Feng Chen. Qualitative analysis and new traveling wave solutions for the stochastic Biswas-Milovic equation[J]. AIMS Mathematics, 2025, 10(2): 4092-4119. doi: 10.3934/math.2025190

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Abstract

In this paper, we investigated the planar dynamical system and new traveling wave solution of the stochastic Biswas-Milovic equation (BME) with dual-power law nonlinearity and multiplicative white noise in the Itô sense. First, the stochastic BME with dual-power law nonlinearity and multiplicative white noise in the Itô sense was transformed into a nonlinear ordinary differential equation (NLODE) through traveling wave transformation. Second, the dynamical bifurcation conditions and phase diagrams of the equation considered were obtained through the method of planar dynamical systems, and the phase portrait of the dynamical system was given. Moreover, taking into account the periodic disturbances in real-world environments, we extended our analysis to explore the effects of disturbance terms. Meanwhile, two-dimensional (2D) and three-dimensional (3D) phase portraits, sensitivity analyses, and the Poincaré section of its perturbed system were plotted through Maple software. Finally, the new traveling wave solutions of the stochastic BME with dual-power law nonlinearity and multiplicative white noise in the Itô sense were constructed by using the complete discrimination system method.

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