Submitting Campus

Daytona Beach

Department

Department of Mathematics

Document Type

Article

Publication/Presentation Date

10-2016

Abstract/Description

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 sech2 soliton and eventually growing back to a narrower and higher amplitude bifurcated Peregrine-type soliton.

Publication Title

Advances and Applications in Fluid Dynamics

DOI

https://doi.org/10.17654/FM019020379

Publisher

Pushpa Publishing House

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