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

Speaker：刘 勇 （华北电力大学）

Time：2017年12月27日   上午 11:05--12:05

Room：东区管理科研楼  数学科学学院1208室

Abstract：The KP-I equation isan important dispersive equation appearing in many physical contexts. It isalso a classical 2+1 dimensional integrable system. Its one dimensionalreduction is the well-known KdV equation

In this talk, we discuss the nonlinearstability of the classical lump solution to the KP-I equation. We investigatethe Backlund transformation associated to this lump. Based on this, we showthat the lump solution is nondegenerated in the sense that the correspondinglinearized KP-I operator does not have nontrivial kernel. Generalizing thisargument, we also prove that a particular family of $y$-periodic solitonsolutions connected to lump is nondegenerated in suitable sense. Finally, usingthese results, we prove that the Morse index of the lump solution is equal toone and the lump is orbitally stable. The question of asymptotical stability remainsopen. This is joint work with Juncheng Wei from UBC.