Water-wave gap solitons: an approximate theory and numerical solutions of the exact equations of motion.
It is demonstrated that a standard coupled-mode theory can successfully describe weakly nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this theory are in reasonable agreement with numerical simulations of the exact equations of motion for ideal planar potential free-surface flows, even for strongly nonlinear waves. In numerical experiments, self-localized groups of nearly standing water waves can exist up to hundreds of wave periods. Generalizations of the model to the three-dimensional case are also derived.
Ruban
V P
VP
Landau Institute for Theoretical Physics, 2 Kosygin Street, 119334 Moscow, Russia. ruban@itp.ac.ru