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arXiv · 2006.11813

Lie symmetries and similarity solutions for the generalized Zakharov equations

K. Krishnakumar·A. Durga Devi·A. Paliathanasis
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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.

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K. Krishnakumar, A. Durga Devi, A. Paliathanasis. 2020-06-21. Lie symmetries and similarity solutions for the generalized Zakharov equations. https://arxiv.org/abs/2006.11813

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