New traveling wave solutions, phase portrait and chaotic patterns for the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise

Da Shi; Zhao Li; Dan Chen; Da Shi; Zhao Li; Dan Chen

doi:10.3934/math.20241257

AIMS Mathematics

2024, Volume 9, Issue 9: 25732-25751. doi: 10.3934/math.20241257

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Research article

New traveling wave solutions, phase portrait and chaotic patterns for the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise

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

Received: 13 May 2024 Revised: 30 August 2024 Accepted: 02 September 2024 Published: 04 September 2024
MSC : 35B20, 35C05, 35C07, 35C09

This article studied the new traveling wave solutions of the cascaded model with higher-order dispersion effects combined with the effects of spatiotemporal dispersion and multiplicative white noise. In the process of exploring traveling wave solutions, a clever combination of the polynomial complete discriminant system was used to discover more forms of traveling wave solutions for this equation. In order to better observe and analyze the propagation characteristics of traveling wave solutions, we used Maple and Matlab software to provide two-dimensional and three-dimensional visualization displays of the equation solutions. Meanwhile, we also analyzed the internal mechanism of nonlinear partial differential equations using planar dynamical systems. The research results indicated that there are differences in the results of different forms of soliton solutions affected by external random factors, which provided more beneficial references for people to better understand the cascaded model with higher-order dispersion effects combined with the effects of spatiotemporal dispersion and multiplicative white noise, and helped people to more comprehensively understand the propagation characteristics of optical solitons. The solution method in this article was also applicable to the study of other nonlinear partial differential equations.
- dispersive concatenation model,
- phase portraits,
- spatio-temporal dispersion,
- complete discriminant system,
- multiplicative white noise,
- traveling wave solutions
Citation: Da Shi, Zhao Li, Dan Chen. New traveling wave solutions, phase portrait and chaotic patterns for the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise[J]. AIMS Mathematics, 2024, 9(9): 25732-25751. doi: 10.3934/math.20241257

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Abstract

This article studied the new traveling wave solutions of the cascaded model with higher-order dispersion effects combined with the effects of spatiotemporal dispersion and multiplicative white noise. In the process of exploring traveling wave solutions, a clever combination of the polynomial complete discriminant system was used to discover more forms of traveling wave solutions for this equation. In order to better observe and analyze the propagation characteristics of traveling wave solutions, we used Maple and Matlab software to provide two-dimensional and three-dimensional visualization displays of the equation solutions. Meanwhile, we also analyzed the internal mechanism of nonlinear partial differential equations using planar dynamical systems. The research results indicated that there are differences in the results of different forms of soliton solutions affected by external random factors, which provided more beneficial references for people to better understand the cascaded model with higher-order dispersion effects combined with the effects of spatiotemporal dispersion and multiplicative white noise, and helped people to more comprehensively understand the propagation characteristics of optical solitons. The solution method in this article was also applicable to the study of other nonlinear partial differential equations.

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