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math.AP2022
The Cauchy problem of the Camassa-Holm equation in a weighted Sobolev space: Long-time and Painlevé asymptotics
Kai Xu, Yiling Yang, Engui Fan
Based on the -generalization of the Deift-Zhou steepest descent method, we extend the long-time and Painlevé asymptotics for the Camassa-Holm (CH) equation to th…
math.AP2022★ 1 cited
Existence of global solutions for the modified Camassa-Holm equation with a nonzero background
Yiling Yang, Engui Fan, Yue Liu
Consideration in the present paper is the existence of global solutions for the modified Camassa-Holm (mCH) equation with a nonzero background initial value. The mCH equation is co…
nlin.SI2022★ 2 cited
On the long-time asymptotics of the modified Camassa-Holm equation with step-like initial data
Yiling Yang, Gaozhan Li, Engui Fan
We study the long time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation with step-like initial data \begin{align} &m_{t}+\left(m\left(u^{2}-u_…