Modulation Analysis of the Stochastic Camassa–Holm Equation with Pure Jump Noise
Journal of Nonlinear Science(2024)
摘要
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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关键词
Stochastic Camassa–Holm equation,Pure jump noise,Random modulation,Solitary waves,60H15,60F05,35R60
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