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 |
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Keywords
- Higher-order KdV equations
- solitary water waves
- soliton-like solutions
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
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 journal › Article
}
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
AN - SCOPUS:78651566343
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 -