### 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 |
---|---|

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Nonlinear Mathematical Physics |

Volume | 16 |

Issue number | SUPPL. 1 |

Publication status | Published - Nov 2009 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Nonlinear Mathematical Physics*,

*16*(SUPPL. 1), 1-12.

**The shape of soliton-like solutions of a higher-order KdV equation describing water waves.** / Andriopoulos, Kostis; Bountis, Tassos; Van Der Weele, K.; Tsigaridi, Liana.

Research output: Contribution to journal › Article

*Journal of Nonlinear Mathematical Physics*, vol. 16, no. SUPPL. 1, pp. 1-12.

}

TY - JOUR

T1 - The shape of soliton-like solutions of a higher-order KdV equation describing water waves

AU - Andriopoulos, Kostis

AU - Bountis, Tassos

AU - Van Der Weele, K.

AU - Tsigaridi, Liana

PY - 2009/11

Y1 - 2009/11

N2 - 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.

AB - 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.

KW - Higher-order KdV equations

KW - solitary water waves

KW - soliton-like solutions

UR - http://www.scopus.com/inward/record.url?scp=78651566343&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651566343&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 1

EP - 12

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

SN - 1402-9251

IS - SUPPL. 1

ER -