Long-time asyptotics behavior for the integrable modified Camassa-Holm equation with cubic nonlinearity
Abstract
In this paper, we investigate the long-time asymptotic behavior of the solution to the initial value problem for the modified Camassa-Holm (mCH) equation with cubic nonlinearity. The equation is known to be integrable, which we mean it admits an Lax pair. We formulate the initial value problem as an associate vector Riemann-Hilbert problem, which allows us to give a parametric representation of the solution to the initial value problem in terms of the solution of the Riemann-Hilbert problem. And then by adopting the nonlinear steepest descent method, we can get the explicit leading order asymptotic of the solution as time goes to infinity.
Cite
@article{arxiv.1911.12554,
title = {Long-time asyptotics behavior for the integrable modified Camassa-Holm equation with cubic nonlinearity},
author = {Jian Xu and Engui Fan},
journal= {arXiv preprint arXiv:1911.12554},
year = {2019}
}
Comments
This result was reported in the forth China-Japan Joint Workshop on Integrable Systems held on August 19-22, 2019