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

Kostis Andriopoulos, Tassos Bountis, K. Van Der Weele, Liana Tsigaridi

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-12
Number of pages12
JournalJournal of Nonlinear Mathematical Physics
Volume16
Issue numberSUPPL. 1
Publication statusPublished - Nov 2009
Externally publishedYes

Fingerprint

Soliton-like Solutions
Higher order equation
water waves
KdV Equation
Water Waves
solitary waves
Solitary Waves
Generalized KdV Equation
Higher Order
Wave Speed
Solitary Wave Solution
Shallow Water
Korteweg-de Vries Equation
Generalized Equation
Small Parameter
Solitons
propagation velocity
shallow water
Propagation
Water

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Andriopoulos, K., Bountis, T., Van Der Weele, K., & Tsigaridi, L. (2009). The shape of soliton-like solutions of a higher-order KdV equation describing water waves. 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.

In: Journal of Nonlinear Mathematical Physics, Vol. 16, No. SUPPL. 1, 11.2009, p. 1-12.

Research output: Contribution to journalArticle

Andriopoulos, K, Bountis, T, Van Der Weele, K & Tsigaridi, L 2009, 'The shape of soliton-like solutions of a higher-order KdV equation describing water waves', Journal of Nonlinear Mathematical Physics, vol. 16, no. SUPPL. 1, pp. 1-12.
Andriopoulos K, Bountis T, Van Der Weele K, Tsigaridi L. The shape of soliton-like solutions of a higher-order KdV equation describing water waves. Journal of Nonlinear Mathematical Physics. 2009 Nov;16(SUPPL. 1):1-12.
Andriopoulos, Kostis ; Bountis, Tassos ; Van Der Weele, K. ; Tsigaridi, Liana. / The shape of soliton-like solutions of a higher-order KdV equation describing water waves. In: Journal of Nonlinear Mathematical Physics. 2009 ; Vol. 16, No. SUPPL. 1. pp. 1-12.
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