Lie symmetries and similarity solutions for the generalized Zakharov equations
Exactly Solvable and Integrable Systems
2020-06-23 v1
Abstract
The theory of Lie point symmetries is applied to study the generalized Zakharov system with two unknown parameters. The system reduces into a three-dimensional real value functions system, where we find that admits five Lie point symmetries. From the resulting point, we focus on these which provide travel-wave similarity transformation. The reduced system can be integrated while we remain with a system of two second-order nonlinear ordinary differential equations. The parameters of the latter system are classified in order the equations to admit Lie point symmetries. Exact travel-wave solutions are found, while the generalized Zakharov system can be described by the one-dimensional Ermakov-Pinney equation.
Keywords
Cite
@article{arxiv.2006.11813,
title = {Lie symmetries and similarity solutions for the generalized Zakharov equations},
author = {K. Krishnakumar and A. Durga Devi and A. Paliathanasis},
journal= {arXiv preprint arXiv:2006.11813},
year = {2020}
}