报告人：刘跃（德克萨斯大学阿林顿）
报告时间：2025年5月28日（星期三）8:30-10:00
2025年5月29日（星期四）8:30-10:00
报告地点：科技楼南楼705
报告摘要：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.
Part one: In the first talk, we shall mainly explain how the above mentioned two methods could be applied to prove orbital stability of simple solitons.
Part two: In the second talk, we focus on multi-solitons and generalized multi-solitons, especially the breathers.
邀请人：李骥
