February 21, 2024Open Access

A Riemann-Hilbert approach to the two-component modified Camassa-Holm equation on the line

KXKai XuSuranaree University of Technology LJLuman JuFudan University EFEngui FanZhejiang Normal University

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Abstract

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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Cite This Study

Xu et al. (Wed,) studied this question.

synapsesocial.com/papers/68e785a2b6db6435876f7d86 https://doi.org/https://doi.org/10.48550/arxiv.2402.13620

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