The mKdV equation under the Gaussian white noise and Wiener process: Darboux transformation and stochastic soliton solutions

Rui-rui Yuan, Ying Shi, Song-lin Zhao and Wen-zhuo Wang

Chaos, Solitons & Fractals, 2024, vol. 181, issue C

Abstract: In this paper, we propose a novel integrable system named the stochastic mKdV equation, along with its corresponding Lax pair. We aim to extend the methodology of deterministic integrable systems to construct and solve stochastic integrable systems. The Darboux transformation effectively obtains analytic solutions for the integrable stochastic mKdV equation. Using the Darboux transformation, soliton solutions incorporating stochastic terms are obtained as Wronskian determinants. Furthermore, we conduct an in-depth analysis of the dynamics exhibited by the stochastic one-soliton and the two-soliton solutions.

Keywords: Stochastic mKdV equation; Gaussian white noise; Darboux transformation; Stochastic soliton solutions (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002613

DOI: 10.1016/j.chaos.2024.114709

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