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.

Keywords

Bibliographic record

BibTeX Citation

@article{Vuillon2018somespecial,
  author = {Vuillon, L. and Dutykh, D. and Fedele, F.},
  title = {Some special solutions to the Hyperbolic NLS equation},
  journal = {Comm. Nonlinear Sci. Numer. Simulat.},
  year = {2018},
  volume = {57},
  pages = {202--220},
  doi = {10.1016/j.cnsns.2017.09.018},
  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.},
  keywords = {deep water waves, wave patterns, Hyperbolic equations, NLS equation}
}