November  2004, 4(4): 911-920. doi: 10.3934/dcdsb.2004.4.911

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

1. 

Institute of Mechanics, Vienna University of Technology, A-1040 Vienna, Austria

2. 

Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

3. 

Department of Mathematics and Computer Science, University of Leicester, Leicester, LE1 7RH

Received  February 2003 Revised  December 2003 Published  August 2004

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.
Citation: A. Berger, R.S. MacKay, Vassilis Rothos. A criterion for non-persistence of travelling breathers for perturbations of the Ablowitz--Ladik lattice. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 911-920. doi: 10.3934/dcdsb.2004.4.911
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