Orbital stability of the modified Camassa-Holm equation




报告题目:Orbital stability of the modified Camassa-Holm equation




报告摘要:We study the stability of smooth and peaked solitary waves to the modified Camassa-Holm equation. This quasilinear equation with cubic nonlinearity is completely integrable and arises as a model for the unidirectional propagation of shallow water waves. Based on the phase portrait analysis, we demonstrate the existence of unique localized smooth solitary-wave solution with certain range of the linear dispersive parameter. We then show orbital stability of the smooth solitary wave solution under small disturbances by means of variational methods, considering a minimization problem with an appropriate constraint. Using the variational approach with suitable conservation laws, we also establish the orbital stability of peakons in the Sobolev space H1W1,4 without the assumption on the positive momentum density initially. Finally we demonstrate spectral stability of such smooth solitary waves using refined spectral analysis of the linear operator corresponding to the second-order variational derivative of the local Hamiltonian.


报告人简介:李骥,华中科技大学数学与统计学院教授,博士生导师,2008年本科毕业于南开大学数学试点班,2012年在美国杨伯翰大学取得博士学位,后在明尼苏达大学和密西根州立大学做博士后。主要研究几何奇异摄动理论及应用和相应的随机扰动理论,以及浅水波孤立子稳定性问题。在TAMS , JMPAJFAJDEPhyD等杂志发表论文二十余篇。