We consider the stationary solutions for a class of Schrödinger 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, in the limit of large focusing nonlinearity we prove that the ground state stationary solutions consist of N wavefunctions localized on a single well. Furthermore, we consider in detail the case of N = 4 wells, where we show the occurrence of spontaneous symmetry-breaking bifurcation effect.

Nonlinear Schrödinger equations with multiple-well potential / Sacchetti, Andrea. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - STAMPA. - 241:(2012), pp. 1815-1824. [10.1016/j.physd.2012.08.015]

Nonlinear Schrödinger equations with multiple-well potential

SACCHETTI, Andrea
2012

Abstract

We consider the stationary solutions for a class of Schrödinger 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, in the limit of large focusing nonlinearity we prove that the ground state stationary solutions consist of N wavefunctions localized on a single well. Furthermore, we consider in detail the case of N = 4 wells, where we show the occurrence of spontaneous symmetry-breaking bifurcation effect.
241
1815
1824
Nonlinear Schrödinger equations with multiple-well potential / Sacchetti, Andrea. - In: PHYSICA D-NONLINEAR PHENOMENA. - ISSN 0167-2789. - STAMPA. - 241:(2012), pp. 1815-1824. [10.1016/j.physd.2012.08.015]
Sacchetti, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/876289
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