Graduate School in Nonlinear Science

Sponsored by The Danish ResearchAgency

MIDIT                              OFD                          CATS
Modelling, Nonlinear Dynamics      Optics and Fluid Dynamics    Chaos and Turbulence Studies
and Irreversible Thermodynamics    Risø National Laboratory     Niels Bohr Institute and
Technical University of Denmark    Building 128                 Department of Chemistry
Building 321                       P.O. Box 49                  University of Copenhagen
DK-2800 Lyngby                     DK-4000 Roskilde             DK-2100 Copenhagen Ø
Denmark                            Denmark                      Denmark


by Annalisa Calini
Department of Mathematics,
College of Charleston
Charleston SC, USA

MIDIT-seminar 507

Thursday, May 30, 2002, 16.00 h
at IMM, Bldg. 305, Room 130, DTU

Abstract: In this work with C. Schober (ODU), we numerically investigate dispersive perturbations of the nonlinear Schroedinger (NLS) equation, which model waves in deep water. We observe that a chaotic regime greatly increases the likelihood of rogue wave formation. These large amplitude waves are well modeled by higher order homoclinic solutions of the NLS equation for which the spatial excitations have coalesced to produce a wave of maximal amplitude. A Melnikov analysis of the conditions for the onset of chaos identifies the observed maximal amplitude homoclinic solutions as the persistent hyperbolic structures throughout the perturbed dynamics.