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A REMARK ON THE EXISTENCE OF BREATHER SOLUTIONS FOR THE DISCRETE NONLINEAR SCHRÖDINGER EQUATION IN INFINITE LATTICES: THE CASE OF SITE-DEPENDENT ANHARMONIC PARAMETERS

Published online by Cambridge University Press:  02 February 2006

Nikos I. Karachalios
Nikos I. Karachalios
Affiliation:
Department of Mathematics, University of the Aegean, Karlovassi GR 83200, Samos, Greece ([email protected])
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Abstract

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We discuss the existence of breather solutions for a discrete nonlinear Schrödinger equation in an infinite $N$-dimensional lattice, involving site-dependent anharmonic parameters. We give a simple proof of the existence of (non-trivial) breather solutions based on a variational approach, assuming that the sequence of anharmonic parameters is in an appropriate sequence space (decays with an appropriate rate). We also give a proof of the non-existence of (non-trivial) breather solutions, and discuss a possible physical interpretation of the restrictions, in both the existence and non-existence cases.

Keywords

Primary 37L6035Q5547J30discrete nonlinear Schrödinger equationlattice differential equationsbreather solutionsvariational methods
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 115 - 129
Copyright
Copyright © Edinburgh Mathematical Society 2006