# American Institute of Mathematical Sciences

2015, 2015(special): 981-989. doi: 10.3934/proc.2015.0981

## Symmetries and solutions of a third order equation

 1 Instituto de Matemática, Estatística e Computação Cie ntífica, IMECC - UNICAMP, Sérgio Buarque de Holanda, 651, 13083-859, Campinas, SP, Brazil 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  September 2014 Revised  January 2015 Published  November 2015

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.
Citation: Júlio Cesar Santos Sampaio, Igor Leite Freire. Symmetries and solutions of a third order equation. Conference Publications, 2015, 2015 (special) : 981-989. doi: 10.3934/proc.2015.0981
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