### Abstract

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 |

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*Proceedings of the Royal Society A*,

*469*(2150), [20120485]. https://doi.org/10.1098/rspa.2012.0485

**Steady dark solitary flexural gravity waves.** / Milewski, Paul A.; Vanden-Broeck, Jean-Marc; Wang, Zhan.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A*, vol. 469, no. 2150, 20120485. https://doi.org/10.1098/rspa.2012.0485

}

TY - JOUR

T1 - Steady dark solitary flexural gravity waves

AU - Milewski, Paul A.

AU - Vanden-Broeck, Jean-Marc

AU - Wang, Zhan

PY - 2013/2

Y1 - 2013/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84872281757&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1098/rspa.2012.0485

U2 - 10.1098/rspa.2012.0485

DO - 10.1098/rspa.2012.0485

M3 - Article

VL - 469

JO - Proceedings of the Royal Society A

JF - Proceedings of the Royal Society A

SN - 0080-4630

IS - 2150

M1 - 20120485

ER -