Nonlinear Schrödinger equations with multiple-well potential

We consider the stationary solutions for a class of Schrödinger equations with a NN-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 NN-dimensional Hamiltonian system, where the coupling term among the coordinates is a tridiagonal Toeplitz matrix. In particular, in the limit of large focusing nonlinearity we prove that the ground state stationary solutions consist of NN wavefunctions localized on a single well. Furthermore, we consider in detail the case of N=4N=4 wells, where we show the occurrence of spontaneous symmetry-breaking bifurcation effect.

► Semiclassical analysis of quantum systems, like BECs, in a finite lattice. ► Reduction to finite-dimensional dynamical systems by semiclassical methods. ► Explicit solution of stationary ground states obtained for four cells lattices. ► Analysis of the spontaneous symmetry bifurcation effect. ► Localization effect on a single cell lattice for large focusing nonlinearities.