DIM-CMM Universidad de Chile

email:

**Abstract**: In this talk I will describe a construction of new
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 to 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.

This is joint work with Michal Kowalczyk, Frank Pacard and Juncheng Wei.