Symmetries and conservation laws of a KdV6 equation

María Santos Bruzón; Tamara María Garrido

doi:10.3934/dcdss.2018038

Article Contents

2018, Volume 11, Issue 4: 631-641. Doi: 10.3934/dcdss.2018038

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Symmetries and conservation laws of a KdV6 equation

María Santos Bruzón^, and
Tamara María Garrido

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

* Corresponding author: M.S. Bruzón.
* Corresponding author: M.S. Bruzón.

Received: December 2016

Revised: May 2017

Published: August 2018

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Abstract

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.

Keywords:

KdV6,
Lie group analysis,
classical symmetries,
nonclassical symmetries,
conservation laws and classical potential symmetries.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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References

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