Nonlinear Schrodinger Equation, Allen-Cahn Equation and Toda System

Abstract: In this talk I will describe a new construction of solutions to some classical autonomous semilinear elliptic equations in the plane. These solutions constitute a "gluing" of one-dimensional profiles with a single transition, located very far apart one from each other. In the case of the Allen-Cahn equation, solutions with a finite number of nearly parallel transition layers are built, while for the stationary nonlinear Schrodinger equation multiple bump-line patterns are found. The Toda system is shown to rule the asymptotic shape of these transition lines. A connection with Constant mean Curvature Surfaces will be discussed. (joint work with M. del Pino, M. Kowalczyk and F. Pacard.)

Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).