Title: Center manifold approximation to breathers in inhomogeneous lattices.

Author: B Sánchez-Rey
with G James and J Cuevas

Abstract:

By applying a center manifold reduction technique small amplitude breather solutions of a Klein-Gordon lattice with small inhomogeneities can be approximated by homoclinic orbits of a nonlinear two-dimensional map.

In the case of a single mass defeat, we compare the amplitudes of the homoclinic orbit computed numerically with exact breather solutions obtained using the standard method based on the anticontinuous limit. For hard on-site potentials we have found that the range of validity of the center manifold approximation strongly depends on the symmetry of the potential. If the on-site potential is even the approximation is excellent even for large values of the mass defeat. However the range of validity reduces significantly when that symmetry is broken.

In the case of soft potentials the scenario is far more complex and richer due to the intricate structure of the intersections between the stable and unstable manifolds. Using geometrical arguments we are able to predict and explain bifurcations of death and birth of homoclinic points which correspond very accurately with bifurcations of exact breather solutions of the inhomogeneous Klein-Gordon system.

Sevilla, December 17, 2006.