Some special solutions to the Hyperbolic NLS equation
Classical Physics
2020-02-20 v3 Analysis of PDEs
Pattern Formation and Solitons
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.
Cite
@article{arxiv.1307.5507,
title = {Some special solutions to the Hyperbolic NLS equation},
author = {Laurent Vuillon and Denys Dutykh and Francesco Fedele},
journal= {arXiv preprint arXiv:1307.5507},
year = {2020}
}
Comments
33 pages, 10 figures, 70 references. Other author's papers can be found at http://www.denys-dutykh.com/