We study the existence of standing waves for a class of nonlinear Schrodinger equations in R-n, with both an electric and a magnetic field. Under suitable non-degeneracy assumptions on the critical points of an auxiliary function related to the electric field, we prove the existence and the multiplicity of complex-valued solutions in the semiclassical limit. We show that, in the semiclassical limit, the presence of a magnetic field produces a phase in the complex wave, but it does not influence the location of peaks of the modulus of these waves

Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields

Cingolani S.
;
2002-01-01

Abstract

We study the existence of standing waves for a class of nonlinear Schrodinger equations in R-n, with both an electric and a magnetic field. Under suitable non-degeneracy assumptions on the critical points of an auxiliary function related to the electric field, we prove the existence and the multiplicity of complex-valued solutions in the semiclassical limit. We show that, in the semiclassical limit, the presence of a magnetic field produces a phase in the complex wave, but it does not influence the location of peaks of the modulus of these waves
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/206241
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