报告题目： Classification and spectral properties of lump type solutions to the KP-I equation

报告时间：12月19日下午15:00-15:40

报告地点：数统楼311会议室

报告人：刘勇教授 中国科学技术大学

报告摘要：

  KP-I equation is an important integrable PDE. The lump solution of KP-I equation is a travelling wave solution decaying at an algebraic rate and orbitally stable. It turns out that the KP-I equation also has other lump type solutions which have higher energy. While there are several methods constructing these solutions, their classification has not been thoroughly studied before. In this talk, we will show that lump type solutions can be classified in terms of the degree of their tau functions. We also discuss the spectral properties (nondegeneracy and Morse index) of these solutions. This is joint work with Juncheng Wei and Wen Yang.

报告人简介：

  刘勇，中国科学技术大学教授。博士毕业于北京大学数学科学学院，曾在智利大学数学中心从事博士后工作。从事非线性分析和椭圆方程领域相关问题的研究。近年来，主要研究与几何或物理相关的方程，如Allen-Cahn、Ginzburg-Landau、Kadomtsev-Petviashvili、Gross-Pitaevskii等方程解的存在性，稳定性，分类等问题。在ARMA, Crelle's Journal, Advance, SIAM等杂志上发表文章多篇。