The complex mKdV equation with step-like initial data: Large time asymptotic analysis

2022/08/03 by Wang, Zhaoyu, Xu, Kai, Fan, Engui
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2208.01856

Abstract

In this paper, we study large-time asymptotics for the complex modified Korteveg-de Vries equation u_t + (1)/(2)u_xxx+3|u|² u_x=0, with the step-like initial data u(x,0)=u₀(x)= \begincases 0, amp; x ≥ 0,
A e^iBx, amp;x lt; 0. \endcases It is shown that the step-like initial problem can be described by a matrix Riemann-Hilbert problem. We apply the steepest descent method to obtain different large-time asymptotics in the the Zakharov-Manakov region, a plane wave region and a slow decay region.

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