报告题目 (Title)：Stability of peaked solitary waves for a class of cubic quasilinear shallow-water equations (一类三次拟线性浅水方程的尖峰孤立波的稳定性)
报告人 (Speaker)： 狄华斐 教授（广州大学）
报告时间 (Time)：2025年3月20日(周四) 13：00
报告地点 (Place)：腾讯会议：222-381-614
邀请人(Inviter)：朱佩成教授
主办部门：理学院数学系
报告摘要：This talk is concerned with two classes of cubic quasilinear equations, which can be derived as asymptotic models from shallow-water approximation to the 2D incom pressible Euler equations. One class of the models has homogeneous cubic nonlinearity and includes the integrable modified Camassa–Holm (mCH) equation and Novikov equation, and the other class encompasses both quadratic and cubic nonlinearities. It is demonstrated here that both these models possess localized peaked solutions. By constructing a Lyapunov function, these peaked waves are shown to be dynamically stable under small perturbations in the natural energy space H1, without restriction on the sign of the momentum density. In particular, for the homogeneous cubic nonlinear model, we are able to further incorporate a higher-order conservation law to conclude orbital stability in H1 ∩ W1,4. Our analysis is based on a strong use of the conservation laws, the introduction of certain auxiliary functions, and a refined continuity argument.
