Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A criterion for non-persistence of travelling breathers for perturbations of the Ablowitz--Ladik lattice

Pages: 911 - 920, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.911

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A. Berger - Institute of Mechanics, Vienna University of Technology, A-1040 Vienna, Austria (email)
R.S. MacKay - Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom (email)
Vassilis Rothos - Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH, United Kingdom (email)

Abstract: The Ablowitz-Ladik lattice has a two-parameter family of travelling breathers. We derive a necessary condition for their persistence under perturbations of the system. From this we deduce non-persistence for a variety of examples of perturbations. In particular, we show that travelling breathers do not persist under many reversible perturbations unless an additional symmetry is preserved, and we address the case of Hamiltonian perturbations.

Keywords:  Travelling breather, Hamiltonian lattice, first integral.
Mathematics Subject Classification:  Primary: 37K60; Secondary: 34L40, 37L60.

Received: February 2003;      Revised: December 2003;      Available Online: August 2004.