Orbital Stability of Breathers in the Modified Camassa-Holm Equation

Description

The modified Camassa-Holm equation (mCH) with a cubic nonlinearity is an integrabel and nonlocal mathematical model for the unidirectional propagation of shallow- water waves. This study establishes the existence of time-periodic, spatially localized smooth-wave solutions, known as breathers, within a specific range of the linear dispersive parameter. By employing three rarely used conserved quantities, expressed in terms of the momentum variable m, it is demonstrated that breathers, as solutions to the mCH equation, are orbitally stable under perturbations in the Sobolev space H2.

Speaker Biography

Prof. Li is a Professor at Huazhong University of Science and Technology since 2016. Over the years, he has done collaborative work in random dynamical system, multi-scale dynamical system, pattern formation and stability of multi-solitons. Prof.Li has received several grants over the past years, including Oversea outstanding young scholars program, sub project of Key research and development, NSFC general program, Tianyuan visiting scholar program, and Basic research project of HUST, as principal investigator. His current research focus is mainly existence and stability of complicated patterns including multi-solitons, breathers, defected spatial rolls, et.al.