Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term

María  Rosa; María de los Santos  Bruzón; María de la Luz  Gandarias

doi:10.3934/dcdss.2015.8.1331

Article Contents

2015, Volume 8, Issue 6: 1331-1339. Doi: 10.3934/dcdss.2015.8.1331

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Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term

1.
Dpto. de Matemáticas, Universidad de Cádiz, Polígono del Río San Pedro s/n 11510 Puerto Real, Cádiz

Received: May 31, 2015

Revised: July 31, 2015

Published: November 2015

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Abstract

Memory effect in diffusion-reaction equation with finite memory transport plays an important role in physical, biological and chemical sciences. In this work we consider a Fisher equation, which has a nonlinear convection term with finite memory transport, from the point of view of Lie classical reductions. By using a direct method we obtain some travelling waves solutions. Furthermore, by using the multipliers method, we derive some nontrivial conservation laws for this equation.

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Mathematics Subject Classification: Primary: 76M60, 92D25; Secondary: 35Q91.

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