We consider the stationary solutions for a class of Schrödinger equations witha symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassicallimit we prove that the reduction to a finite-mode approximation give the stationary solutions,up to an exponentially small term, and that symmetry-breaking bifurcation occurs ata given value for the strength of the nonlinear term. The kind of bifurcation picture onlydepends on the nonlinearity power. We then discuss the stability/instability properties ofeach branch of the stationary solutions. Finally, we consider an explicit one-dimensional toymodel where the double well potential is given by means of a couple of attractive Dirac’sdelta pointwise interactions.

Bifurcation and Stability for Nonlinear SchrödingerEquations with DoubleWell Potential in the SemiclassicalLimit / R., Fukuizumi; Sacchetti, Andrea. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 145(2011), pp. 1546-1594.

I documenti presenti in Iris Unimore sono rilasciati con licenza Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia, salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Powered by IRIS-about IRIS-Utilizzo dei cookie

 Copyright © 2021