Some special solutions to the Hyperbolic NLS equation
Abstract
The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly acccurate Fourier solver.
Domains
Fluid mechanics [physics.class-ph] Fluids mechanics [physics.class-ph] Analysis of PDEs [math.AP] Pattern Formation and Solitons [nlin.PS] Fluid Dynamics [physics.flu-dyn] Atmospheric and Oceanic Physics [physics.ao-ph] Computational Physics [physics.comp-ph] Exactly Solvable and Integrable Systems [nlin.SI] Geophysics [physics.geo-ph] Geophysics [physics.geo-ph] Global Changes Numerical Analysis [math.NA]| Origin | Files produced by the author(s) |
|---|
Loading...
