Symmetries and solutions of a third order equation

Júlio Cesar Santos  Sampaio; Igor Leite  Freire

doi:10.3934/proc.2015.0981

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2015, Volume 2015: 981-989. Doi: 10.3934/proc.2015.0981 open access

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Symmetries and solutions of a third order equation

Júlio Cesar Santos Sampaio^1, and
Igor Leite Freire^2,

1.
Instituto de Matemática, Estatística e Computação Científica, IMECC - UNICAMP, Sérgio Buarque de Holanda, 651, 13083-859, Campinas, SP
2.
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC - UFABC, Rua Santa Adélia, 166, Bairro Bangu, 09.210 -- 170, Santo André, SP

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

In this paper we study a new third order evolution equation discovered a couple of years ago using a genetic programming. We show that the Lie symmetries of this equation corresponds to space and time translations, as well as a dilation on the space of independent variables and another one with respect to the depend variable. From its symmetries, explicit solutions of the equation are obtained, some of them expressed in terms of the solutions of the Airy equation and Abel equation of the second kind. Additionally, by using the direct method we establish three conservation laws for the equation, one of them new.

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Mathematics Subject Classification: Primary: 76M60, 58J70, 35A30, 70G65.

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