The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles  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 , 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.
Advances and Applications in Fluid Dynamics
Pushpa Publishing House
Scholarly Commons Citation
Sajjadi, S. G., & Smith, T. A. (2016). Exact Analytical Solution of Viscous Korteweg-deVries Equation for Water Waves. Advances and Applications in Fluid Dynamics, 19(2). https://doi.org/10.17654/FM019020379