Journal of Nonlinear Mathematical Physics

Volume 16, Issue Supplement 1, March 2013, Pages 1 - 12

The Shape of Soliton-Like Solutions of a Higher-Order Kdv Equation Describing Water Waves

Authors
Kostis Andriopoulos*, Tassos Bountis, K. Van Der Weele
Centre for Research and Applications of Nonlinear Systems, Department of Mathematics, University of Patras, 26500 Patras, Greece
Liana Tsigaridi
Research Centre for Astronomy and Applied Mathematics, Academy of Athens, 4 Soranou-Efesiou Str., 11527 Athens, Greece, lianatsigaridi@yahoo.gr
Corresponding Author
Kostis Andriopoulos
Received 2 June 2009, Accepted 10 August 2009, Available Online 7 January 2021.
DOI
https://doi.org/10.1142/S1402925109000285How to use a DOI?
Keywords
Higher-order KdV equations, soliton-like solutions, solitary water waves
Abstract

We study the solitary wave solutions of a non-integrable generalized KdV equation proposed by Fokas [A. S. Fokas, Physica D87, 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.

Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - Supplement 1
Pages
1 - 12
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925109000285How to use a DOI?
Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Kostis Andriopoulos
AU  - Tassos Bountis
AU  - K. Van Der Weele
AU  - Liana Tsigaridi
PY  - 2021
DA  - 2021/01
TI  - The Shape of Soliton-Like Solutions of a Higher-Order Kdv Equation Describing Water Waves
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 12
VL  - 16
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000285
DO  - https://doi.org/10.1142/S1402925109000285
ID  - Andriopoulos2021
ER  -