Hylomorphic solitons on lattices

Pages: 875 - 897, Volume 28, Issue 3, November 2010

doi:10.3934/dcds.2010.28.875       Abstract        Full Text (282.2K)       Related Articles

Vieri Benci - Dipartimento di Matematica Applicata "U. Dini”, Università di Pisa, via F. Buonarroti 1/c 56127 Pisa, Italy (email)
Donato Fortunato - Dipartimento di Matematica, Università di Bari and INFN sezione di Bari, Via Orabona 4, 70125 Bari, Italy (email)

Abstract: This paper is devoted to the study of solitons whose existence is related to the ratio energy/charge. These solitons are called hylomorphic. In the first part of the paper we prove an abstract theorem on the existence of hylomorphic solitons which can be applied to the main situations considered in literature. In the second part, we apply this theorem to the nonlinear Schrödinger and Klein Gordon equations defined on a lattice.

Keywords:  Q-balls, Hylomorphic solitons, nonlinear Schroedinger equation, nonlinear Klein-Gordon equation.
Mathematics Subject Classification:  47J30, 35J50, 35J08, 37K40.

Received: March 2010;      Revised: April 2010;      Published: April 2010.