带有纯跳跃噪声的随机卡马萨-霍姆方程的调制分析

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED Journal of Nonlinear Science Pub Date : 2024-04-28 DOI:10.1007/s00332-024-10037-3

Yong Chen, Jinqiao Duan, Hongjun Gao, Xingyu Guo

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引用次数: 0

摘要

我们研究了带有纯跳跃噪声的随机卡马萨-霍姆方程。我们证明，如果解的初始条件是无扰动方程的孤波解，则该解分解为随机调制孤波和少量余波之和。此外，我们还推导出了调制参数方程，并证明当跳跃噪声的振幅趋近于零时，余数收敛于随机线性方程的解。

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Modulation Analysis of the Stochastic Camassa–Holm Equation with Pure Jump Noise

We study the stochastic Camassa–Holm equation with pure jump noise. We prove that if the initial condition of the solution is a solitary wave solution of the unperturbed equation, the solution decomposes into the sum of a randomly modulated solitary wave and a small remainder. Moreover, we derive the equations for the modulation parameters and show that the remainder converges to the solution of a stochastic linear equation as amplitude of the jump noise tends to zero.

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来源期刊

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.