Normalized solutions of
the 1-D nonlinear Schordinger equation
报告专家：蒋美跃 教授（大湾区大学）
报告时间：10月29日（周四）下午15:00-16:00
报告地点：国家天元数学西南中心516报告厅
报告摘要：
In this talk we will present an alternative approach to the normalized solutions (λ, u) of the 1-D nonlinear Schordinger equation(problem (1)):
-u"+λu = grad G(u)
∫_R |u|^2 dx = a > 0
with u ∈ R or u ∈ R^2. Given λ > 0, it is easy to see there is a solution u_λ ∈ H^1(R) of
-u"+λu = grad G(u)
which is called a homolinic solution in dynamical systems. We will establish a connection between the problem (1) and a Dirichlet boundary value problem of the equation
-u" = grad G_1(u)
in a finite interval for another G1(u) by elementary arguments. As consequences, some well known results of solutions of problem (1) are recovered and new existence and uniqueness results are obtained.
专家简介：
蒋美跃，1989年在北京大学获理学博士学位，主要研究方向为非线性分析。在Ann. Inst. H. Poincare Anal. Non Linéaire、Bull. London Math. Soc.等国际期刊发表多篇论文，包含了辛几何中Arnold猜测、带障碍Hamilton系统周期解问题、ROF泛函极小问题等。
邀请人：吕克宁
