TY  - JOUR
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
T1  - Compactons and chaos in strongly nonlinear lattices
N2  - We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are superexponentially localized and present an accurate numerical method allowing one 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.
Y1  - 2009
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.79.026209
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Mulansky, Mario
A1  - Ahnert, Karsten
A1  - Pikovskij, Arkadij
A1  - Shepelyansky, Dima L.
T1  - Dynamical thermalization of disordered nonlinear lattices
N2  - We study numerically how the energy spreads over a finite disordered nonlinear one-dimensional lattice, where all linear modes are exponentially localized by disorder. We establish emergence of dynamical thermalization characterized as an ergodic chaotic dynamical state with a Gibbs distribution over the modes. Our results show that the fraction of thermalizing modes is finite and grows with the nonlinearity strength.
Y1  - 2009
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.80.056212
SN  - 1539-3755
ER  -