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
N1 - Funding Information:
We thank Harvey Segur, Kyriakos Hizanidis and Giorgos Kanellopoulos for their interest in our work and useful suggestions. We also thank the anonymous referees for their valuable comments. KA thanks the Swedish–South African Agreement, grant number 60935, for the funding of the trip to Durban where this work was presented at the Workshop on Nonlinear Differential Equations, the University of KwaZulu-Natal, and the Hellenic Scholarships Foundation (IKY) for partial financial support of this work. KvdW and TB acknowledge support from the Carathéodory Programme, grant number C167, of the University of Patras.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
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
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U2 - 10.1142/s1402925109000285
DO - 10.1142/s1402925109000285
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 -