Compactons and Chaos in Strongly Nonlinear Lattices

Details Compactons and Chaos in Strongly Nonlinear Lattices Compactons and Chaos in Strongly Nonlinear Lattices

2008-08-22

arxiv.org/abs/0808.3059v3

Phys. Rev. E 79, 026209 (2009)

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1103/PhysRevE.79.026209

We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find them for an arbitrary nonlinearity index. Compactons evolve from rather general initially localized perturbations and collide nearly elastically, nevertheless on a long time scale for finite lattices an extensive chaotic state is generally observed. Because of the system's scaling, these dynamical properties are valid for any energy.

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