## Abstract

We consider exact nonlinear solitary water waves on a shear flow with an arbitrary distribution of vorticity. Ignoring surface tension, we impose a non-constant pressure on the free surface. Starting from a uniform shear flow with a flat free surface and a supercritical wave speed, we vary the surface pressure and use a continuation argument to construct a global connected set of symmetric solitary waves. This set includes waves of depression whose profiles increase monotonically from a central trough where the surface pressure is at its lowest, as well as waves of elevation whose profiles decrease monotonically from a central crest where the surface pressure is at its highest. There may also be two waves in this connected set with identical surface pressure, only one of which is a wave of depression.

Original language | English |
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Pages (from-to) | 1131-1187 |

Number of pages | 57 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 218 |

Issue number | 2 |

DOIs | |

Publication status | Published - 4 Nov 2015 |

## ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering