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Stability of solitary waves for some problems in quantum mechanics
by
Vladimir Georgiev
Dipartimento di Matematica, Università di Pisa, Via Buonarroti No.2, 56127 Pisa, Italy
Coauthors: Piero D'Ancona
We consider the coupled system of Schrödinger and Poisson equation in a presence of an external Coulomb potential of attractive sign. The existence and multiplicity of solitary waves is established. For the solitary waves minimizing the energy functional we prove the Liapunov stability of these waves. The main tool is the application of suitable dispersive and Strichartz type estimates for the potential perturbations of wave and Schrödinger equation.
Date received: June 27, 2003
Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # calr-51.