报告人：刘跃（德克萨斯大学阿林顿）
报告时间：2025年5月25日（星期日）14:30-16:00
2025年5月26日（星期一）14:30-16:00
报告地点：科技楼南楼705
报告摘要：In the first talk, we shall briefly report a recent asymptotic stability result of smooth solitons and multi-solitons in energy space for the Camassa-Holm (CH) equation. We show that a CH solution initially close to a soliton, once translated, converges weakly in H^1 to a possibly different soliton as time goes to infinity. The proof is motivated by the bi-Hamiltonian structure of the CH equation and a Liouville type theorem for the CH flow close to the solitons.
In the second talk, we show some details about the proof. The new ingredient in the proof of Liouville theorem is by employing the completeness relations of square eigenfunctions of the CH recursion operator. Some applications are presented in classifications of solutions of linear problems related to KdV and mKdV equations. If time permits, I will disscuss also the orbital and asymptotic stability of N-solitons for the modified CH equation.
邀请人：李骥
