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### Abstract

The nonlinear Schrödinger (NLS) equation describes the modulational limit of many surface water wave problems. Dark solitary waves of the NLS equation asymptote to a constant in the far field and have a localized decrease to zero amplitude at the origin, corresponding to water wave solutions that asymptote to a uniform periodic Stokes wave in the far field and decreasing oscillations near the origin. It is natural to ask whether these dark solitary waves can be found in the irrotational Euler equations. In this paper, we find such solutions in the context of flexural-gravity waves, which are often used as a model for waves in ice-covered water. This is a situation in which the NLS equation predicts steadily travelling dark solitons. The solution branches of dark solitons are continued, and one branch leads to fully localized solutions at large amplitudes.

Original language | English |
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Article number | 20120485 |

Journal | Proceedings of the Royal Society A |

Volume | 469 |

Issue number | 2150 |

Early online date | 28 Nov 2012 |

DOIs | |

Publication status | Published - Feb 2013 |

## Fingerprint Dive into the research topics of 'Steady dark solitary flexural gravity waves'. Together they form a unique fingerprint.

## Projects

- 1 Finished

### Nonlinear Hydroelastic Waves with Applications to Ice Sheets

Engineering and Physical Sciences Research Council

12/11/12 → 11/11/15

Project: Research council

## Cite this

Milewski, P. A., Vanden-Broeck, J-M., & Wang, Z. (2013). Steady dark solitary flexural gravity waves.

*Proceedings of the Royal Society A*,*469*(2150), [20120485]. https://doi.org/10.1098/rspa.2012.0485