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Article Dans Une Revue Physical Review Letters Année : 2009

Role of Singular Tori in the Dynamics of Spatiotemporal NonlinearWave Systems

Résumé

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.
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Dates et versions

hal-00428928 , version 1 (30-10-2009)

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Dominique Sugny, Antonio Picozzi, S. Lagrange, Hans-Rudolf Jauslin. Role of Singular Tori in the Dynamics of Spatiotemporal NonlinearWave Systems. Physical Review Letters, 2009, 103 (3), pp.034102. ⟨10.1103/PhysRevLett.103.034102⟩. ⟨hal-00428928⟩
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