The Shape of Soliton-Like Solutions of a Higher-Order Kdv Equation Describing Water Waves
- 10.1142/S1402925109000285How to use a DOI?
- Higher-order KdV equations; soliton-like solutions; solitary water waves
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.
- © 2009 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
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Cite this article
TY - JOUR AU - Kostis Andriopoulos AU - Tassos Bountis AU - K. Van Der Weele AU - Liana Tsigaridi PY - 2021 DA - 2021/01/07 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 - 10.1142/S1402925109000285 ID - Andriopoulos2021 ER -