## Abstract

We study the solitary wave solutions of a non-integrable generalized KdV equation proposed by Fokas [A. S. Fokas, Physica D 87, 145 (1995)], aiming to describe unidirectional waves in shallow water with greater accuracy than the standard KdV equation. This generalized equation includes higher-order terms in the small parameters α and β, representing respectively the height and inverse width of the wave compared to the thickness of the water sheet. The solitary waves we find have a smaller height and a larger width than the corresponding KdV soliton at the same propagation velocity. Extrapolating these results we conjecture that in the limit of arbitrarily high order in α and β the solitary waves will attain a specific, finite height and width as the wave speed c increases.

Original language | English |
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Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Nonlinear Mathematical Physics |

Volume | 16 |

Issue number | SUPPL. 1 |

DOIs | |

Publication status | Published - Nov 2009 |

## Keywords

- Higher-order KdV equations
- solitary water waves
- soliton-like solutions

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics