Traveling wave solutions to the Allen-Cahn equation

Abstract

For the Allen-Cahn equation, it is well known that there is a monotone standing wave joining with the balanced wells of the potential. In this paper we study the existence of traveling wave solutions for the Allen-Cahn equation on an infinite channel. Such traveling wave solutions possess a large number of oscillation and they are obtained with the aid of variational arguments.

References in corpus (1)

• Entire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in ${\mathbb{R}}^3$