Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy


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

HIGHER - ORDER CUBIC NONLINEAR SCHRÖDINGER EQUATION: GENERAL PROPERTIES AND RESONANT SOLITON RADIATION

by V.I. Karpman
Hebrew University, Jerusalem, Israel

Monday October 25, 1999, 13:00 h (NOTE THE TIME CHANGE)
Meeting Room, OFD, Building 130
Risø National Laboratory, Roskilde

Abstract: The resonant radiation of solitons due to higher order dispersion, described by an extended nonlinear Schrödinger (NLS) equation with nonlinear (cubic) dispersive terms and linear terms with third and fourth derivatives, is studied. The basic equation includes, as a particular case, a higher order derivative NLS equation. General properties of the master equation, such as conservation laws, Hamiltonian structures (in important particular cases) and Galilei transformation are studied. Explicit asymptotic expressions, describing the radiation at different initial conditions, are derived. The obtained results, in particular, provide a basis for the study of soliton losses, caused by the radiation, in optical fibers.