Effects of additive noise and variable coefficients on the exact solutions of the stochastic Kawahara equation

IF 2.3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physics Letters A Pub Date : 2025-06-06 DOI:10.1016/j.physleta.2025.130723

Maojie Cai, Changzhao Li, Chuanjian Wang, Jiamin Shi

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引用次数: 0

Abstract

This paper investigates exact solutions and soliton dynamics in a stochastic Kawahara equation with variable coefficients and additive noise. Using Galilean transformation, the original system is transformed to a variable-coefficient equation coupled with a solvable stochastic ODEs. Exact solutions are derived via

Painlev \overset{´}{e}

truncation expansion and validated through an improved Zabusky-Kruskal finite difference scheme. Quantitative analysis reveals that variable coefficients induce waveform deformation through amplitude-phase modulation, while noise governs soliton stability via amplitude-width interactions. Crucially, increasing wave numbers suppress soliton diffusion by amplifying amplitude without altering width, thereby slowing dissipation. The methodology uniquely couples deterministic integrability with stochastic dynamics, differing from conventional approaches. Results demonstrate synergistic effects of nonlinear dispersion, variable coefficients, and noise on soliton evolution, providing new insights for stochastic fifth-order dispersive systems.

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加性噪声和变系数对随机Kawahara方程精确解的影响

研究了随机变系数加性噪声Kawahara方程的精确解和孤子动力学。利用伽利略变换，将原系统转化为带有可解随机ode的变系数方程。通过painlevel截断展开得到精确解，并通过改进的Zabusky-Kruskal有限差分格式进行验证。定量分析表明，变系数通过幅相调制引起波形变形，而噪声通过幅宽相互作用控制孤子的稳定性。至关重要的是，波数的增加通过放大振幅而不改变宽度来抑制孤子扩散，从而减缓耗散。与传统方法不同，该方法独特地将确定性可积性与随机动力学相结合。研究结果证明了非线性色散、变系数和噪声对孤子演化的协同作用，为随机五阶色散系统的研究提供了新的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physics Letters A 物理-物理：综合

CiteScore

5.10

自引率

3.80%

发文量

493

审稿时长

30 days

期刊介绍： Physics Letters A offers an exciting publication outlet for novel and frontier physics. It encourages the submission of new research on: condensed matter physics, theoretical physics, nonlinear science, statistical physics, mathematical and computational physics, general and cross-disciplinary physics (including foundations), atomic, molecular and cluster physics, plasma and fluid physics, optical physics, biological physics and nanoscience. No articles on High Energy and Nuclear Physics are published in Physics Letters A. The journal''s high standard and wide dissemination ensures a broad readership amongst the physics community. Rapid publication times and flexible length restrictions give Physics Letters A the edge over other journals in the field.