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math.AP2023
Long-time asymptotic behavior of the Hunter-Saxton equation
Luman Ju, Kai Xu, Engui Fan
With -generalization of the Deift-Zhou steepest descent method, we investigate the long-time asymptotics of the solution to the Cauchy problem for the Hunter-Saxton…
math.AP2022
The complex mKdV equation with step-like initial data: Large time asymptotic analysis
Zhaoyu Wang, Kai Xu, Engui Fan
In this paper, we study large-time asymptotics for the complex modified Korteveg-de Vries equation \begin{equation} u_t + \frac{1}{2}u_{xxx}+3|u|^2 u_x=0, \end{equation} with the s…