Long time behavior and soliton solution for the Harry Dym equation

[摘要] In this paper, we consider the Harry-Dym equation with the decaying initial data. Using the nonlinear steepest decent method of Deift and Zhou for Riemann-Hilbert problems, we firstly obtain the explicit leading asymptotic of solution of by Harry-Dym equation by transforming its Lax pairs. What'more, in the framework of the Riemann-Hilbert problem, we can find cusp soliton. (C) 2019 Published by Elsevier Inc.

[发布日期] 2019-12-01

[关键词] Harry Dym equation;Riemann-Hilbert problem;Long time asymptotic behavior;Soliton solution