Ground states on a fractured strip and one-dimensional reduction

Abstract

We consider the nonlinear Schrödinger equation on a strip with Neumann boundary conditions and a delta condition at $x=0$. We first show the existence of ground states as minimizers of the action or of the energy under suitable constraints. We then prove that the energy minimizers converge to the ground state on the line with a delta condition as the width of the strip shrinks to zero.