学术讲座【Nondegeneracy and Morse index of multiple-end solutions to the elliptic sine-Gordon equation】
时间：2018年6月23日(星期六)上午10:00-11:00
地点：理工北楼601报告厅
主办：数学与信息学院
主讲：华北电力大学，刘勇副教授
参加对象：数学系相关教师与研究生
专家简介：刘勇， 华北电力大学副教授，硕博士期间师从北京大学蒋美跃教授，博士后合作导师为智利大学的Michal Kowalczyk教授，主要合作者为不列颠哥伦比亚大学的魏军城教授等，主要研究方向为椭圆型偏微分方程，发表论文十余篇，其中多篇在微分方程方向的顶级学术期刊发表，如Advances in Mathematics, Journal of Functional Analysis, Ann. H. Henri. Poincare, J. Math. Pure. App., Analysis & PDE.等。
报告摘要：Allen-Cahn type equations, including the elliptic sine-Gordon equation, are important second order elliptic semi-linear PDEs. In this talk, we first mention some existence and classification results for these equations in general dimension. Then we turn to the special case of elliptic sine-Gordon equation. We classify all the finite Morse index solutions of this equation in the plane using inverse scattering transform. Furthermore, using Backlund transformation, we show that these solutions are nondegenerated. We also prove that those solutions with 2k ends have Morse index k(k-1)/2. This is joint work with Prof. Juncheng Wei.