Nondegeneracy, Morse index and Orbital stability of the lump solution to the KP-I equation

发布时间：2018-01-22 来源：赢咖3 浏览次数：

Speaker:	刘勇	DateTime:	2018年1月26日（周五）上午10:30-11:15
Brief Introduction to Speaker: 刘勇副教授,华北电力大学.		Place:
Abstract: The KP-I equation is an important dispersive equation appearing in many physical contexts. It is also a classical 2+1 dimensional integrable system.Its one dimensional reduction is the well-known KdV equation.In this talk, we discuss the nonlinear stability of the classical lump solution to the KP-I equation. We investigate the Backlund transformationassociated to this lump. Based on this, we show that the lumpsolution is nondegenerated in the sense that the corresponding linearized KP-Ioperator does not have nontrivial kernel. Generalizing this argument, we alsoprove that a particular family of $y$-periodicsoliton solutions connected tolump is nondegenerated in suitable sense.Finally,using these results, weprove that the Morse index of the lump solution is equal to one and the lumpis orbitally stable. The question of asymptotical stability remains open. Thisis joint work with Juncheng Wei from UBC.