Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices

Details Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices

2009-09-18

arxiv.org/abs/0909.3467v1

Mathematics

Dynamical Systems

Scientific paper

We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schroedinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum approximation techniques introduced in [7], actually using its main result as an important lemma.

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