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發布時間:2021-04-25【告訴好友】 【關閉窗口】

  題目:Orbital stability of the modified Camassa-Holm equation



  報告人:李驥 教授 華中科技大學

  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 H1∩W1,4 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.


  李驥,華中科技大學數學與統計學院教授,博士生導師,2008年本科畢業于南開大學數學試點班,2012年在美國楊伯翰大學取得博士學位,后在明尼蘇達大學和密西根州立大學做博士后。主要研究幾何奇異攝動理論及應用和相應的隨機擾動理論,以及潛水波孤立子穩定性問題。在TAMS , JMPA,JFA,JDE,PhyD等雜志發表論文二十余篇。