[10-08] 美国德克萨斯大学阿灵顿分校刘跃教授学术报告
题目:Stability of Solitary Waves to the Shallow Water Models
时间：2022年10月8日（周六）上午9：00-11：00
地点：腾讯会议（会议ID：296-414-553）
报告人：刘跃教授
摘要：In this talk, we will present our recent results on dynamical stability of localized smooth solitary waves to the Camassa-Holm (CH) equation and the modified Camassa-Holm (mCH) equation on the real line. Those quasilinear equations are completely integrable and arise as asymptotic models for the unidirectional propagation of shallow water waves. We show orbital stability of the smooth solitary-wave solution of the mCH equation in the energy space under small disturbances by variational methods without the assumption on the positive momentum density initially. We also demonstrate the dynamical stability of the shapes of all smooth multi-solitons under small disturbances in a suitable Sobolev space. Our approach in the spectral analysis consists in an invariant for the multi-solitons with new operator identities motivated by the bi-Hamilton structure and integrable property of the recursion operator of the CH equation.
报告人简介：刘跃，美国德克萨斯大学阿灵顿分校教授，1994年获布朗大学博士学位，师从国际著名数学家Walter Strauss教授。在偏微分方程，应用分析和流体力学，可积系统与孤子理论，非线性波方程的稳定性理论、奇异性形成、局部和整体适定性等领域取得国际领先的成果。在“Comm. Pure Appl. Math.”、“Adv. Math.”、“Comm. Math. Phys.”、“Arch. Ration.Mech. Anal.”、“J. Funct. Anal.”、“Physica D”、“J. Differential Equations”、“Nonlinearity”、“Quart. of Appl. Math.”等国际著名刊物上发表论文100余篇。
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