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arXiv · 1704.00723

Exact analytical solution of viscous Korteweg-deVries equation for water waves

S. G. Sajjadi·T. A. Smith
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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(ξ) soliton and eventually growing back to a narrower and higher amplitude bifurcated Peregrine-type soliton.

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S. G. Sajjadi, T. A. Smith. 2017-04-07. Exact analytical solution of viscous Korteweg-deVries equation for water waves. https://doi.org/10.17654/fm019020379

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