Nonlinear Schrodinger equations with multiple-well potential

Abstract

We consider the stationary solutions for a class of Schrodinger equations with a N-well potential and a nonlinear perturbation. By means of semiclassical techniques we prove that the dominant term of the ground state solutions is described by a N-dimensional Hamiltonian system, where the coupling term among the coordinates is a tridiagonal Toeplitz matrix. In particular we consider the case of N=4 wells, where we show the occurrence of spontaneous symmetry-breaking bifurcation effect. In particular, in the limit of large focusing nonlinearity we prove that the ground state stationary solutions consist of N wavefunctions localized on a single well.

Accepted on Physica D - Keywords: Nonlinear dynamics, Bifurcation, Semiclassical limit, Bose-Einstein condensates in lattices

References in corpus (2)

• Symmetry-breaking bifurcation in the nonlinear Schrödinger equation with symmetric potentials
• Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit

Cited by in corpus (3)

• Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
• Nonlinear Schrodinger equations with a multiple-well potential and a Stark-type perturbation
• Formation of nonlinear modes in one-dimensional quasiperiodic lattices with a mobility edge