Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems.
We show that the peculiar topological properties inherent to singular tori play a major role in the spatiotemporal dynamics of counterpropagating nonlinear waves. Under rather general conditions, these Hamiltonian wave systems exhibit a relaxation process towards a stationary state. We show that this stationary state converges exponentially towards the singular torus of the associated Liouville-integrable Hamiltonian system in the limit of an infinite medium. The singular torus then appears as an attractor for the infinite dimensional dynamical system, a feature which is illustrated by several key models of spatiotemporal wave interactions.
Sugny
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D
Institut Carnot de Bourgogne, UMR CNRS 5027, BP 47870, 21078 Dijon, France. dominique.sugny@u-bourgogne.fr
Picozzi
A
A
Lagrange
S
S
Jauslin
H R
HR