Exact analytical solution of viscous Korteweg-deVries equation for water waves
Abstract
The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles [4] is revisited. The solution for a one-dimensional gravity wave in a water of uniform depth is considered. This leads to finding the solution to a Korteweg-de Vries (KdV) equation in which the nonlinear term is small. Also considered is the asymptotic solution of the linearized KdV equation both analytically and numerically. As in Miles [4], the asymptotic solution of the KdV equation for both linear and weakly nonlinear case is found using the method of inversescattering theory. Additionally investigated is the analytical solution of viscous-KdV equation which reveals the formation of the Peregrine soliton that decays to the initial sech^2(\xi) soliton and eventually growing back to a narrower and higher amplitude bifurcated Peregrine-type soliton.
Keywords
Cite
@article{arxiv.1704.00723,
title = {Exact analytical solution of viscous Korteweg-deVries equation for water waves},
author = {S. G. Sajjadi and T. A. Smith},
journal= {arXiv preprint arXiv:1704.00723},
year = {2017}
}
Comments
15 pages