A Riemann-Hilbert approach to the two-component modified Camassa-Holm equation on the line
arxiv(2024)
摘要
In this paper, we develop a Riemann-Hilbert approach to the Cauchy problem
for the two-component modified Camassa-Holm (2-mCH) equation based on its Lax
pair. Further via a series of deformations to the Riemann-Hilbert problem
associated with the Cauchy problem by using the ∂̅-generalization
of Deift-Zhou steepest descent method, we obtain the long-time asymptotic
approximations of the solutions of the 2-mCH equation in four space-time
regions. Our results also confirm the soliton resolution conjecture and
asymptotically stability of the N-soliton solutions for the 2-mCH equation.
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