Long-time asymptotic behaviour for the fifth order modified Korteweg-de Vries equation
Mathematical Physics
2019-08-01 v1 Analysis of PDEs
math.MP
Abstract
Following Deift-Zhou's nonlinear steepest descent method, the long-time asymptotic behavior for the Cauchy problem of the 5th order modified Korteweg-de Vries equation is analyzed. Based on the inverse scattering transform, the 5th order MKdV is transformed to a 2 by 2 oscillatory Riemann-Hilbert problem, then by manipulating the Cauchy operator and reducing the degree of the phase function, the long-time asymptotics of the solution is given in terms of solutions of the parabolic cylinder equation.
Keywords
Cite
@article{arxiv.1907.13243,
title = {Long-time asymptotic behaviour for the fifth order modified Korteweg-de Vries equation},
author = {Fudong Wang and Wen-Xiu Ma},
journal= {arXiv preprint arXiv:1907.13243},
year = {2019}
}