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

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  • 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.
    Mathematics Subject Classification: Primary: 37K60; Secondary: 34L40, 37L60.

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