# American Institute of Mathematical Sciences

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August  2018, 11(4): 631-641. doi: 10.3934/dcdss.2018038

## Symmetries and conservation laws of a KdV6 equation

 Department of Mathematics, University of Cádiz, PO.BOX 40, 11510 Puerto Real, Cádiz, Spain

* Corresponding author: M.S. Bruzón.

Received  December 2016 Revised  May 2017 Published  November 2017

In the present work we make an analysis of the Korteweg-de Vries of sixth order. We apply the classical Lie method of infinitesimals and the nonclassical method, due to Bluman and Cole, to deduce new symmetries of the equation which cannot be obtained by Lie classical method. Moreover, we obtain ten different conservation laws depending on the parameters and we conclude that potential symmetries project on the infinitesimals corresponding to the classical symmetries.

Citation: María Santos Bruzón, Tamara María Garrido. Symmetries and conservation laws of a KdV6 equation. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 631-641. doi: 10.3934/dcdss.2018038
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