<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Reaction-diffusion equations have enjoyed a considerable amount of scientific interest. The reason for the large amount of work put into studying these equations is not only their practical relevance, but also interesting phenomena that can arise from such equations. Fisher equation is commonly used in biology for population dynamics models and in bacterial growth problems as well as development and growth of solid tumours. The physical aspects of this equation are not fully understood without getting deeper into the concept of conservation laws. In [<xref ref-type="bibr" rid="j_AMNS.2016.2.00026_ref_004_w2aab3b7ab1b6b1ab1b8b4Aa">4</xref>], Anco and Bluman gave a general treatment of a direct conservation law method for partial differential equations expressed in a standard Cauchy-Kovaleskaya form. In this work we study the well known density dependent diffusion-reaction equation. We derive conservation laws by using the direct method of the multipliers.</p></abstract>

Reaction-diffusion equations have enjoyed a considerable amount of scientific interest. The reason for the large amount of work put into studying these equations is not only their practical relevance, but also interesting phenomena that can arise from such equations. Fisher equation is commonly used in biology for population dynamics models and in bacterial growth problems as well as development and growth of solid tumours. The physical aspects of this equation are not fully understood without getting deeper into the concept of conservation laws. In [4], Anco and Bluman gave a general treatment of a direct conservation law method for partial differential equations expressed in a standard Cauchy-Kovaleskaya form. In this work we study the well known density dependent diffusion-reaction equation. We derive conservation laws by using the direct method of the multipliers.

Multiplier method and exact solutions for a density dependent reaction-diffusion equation

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Reaction-diffusion equations have enjoyed a considerable amount of scientific interest. The reason for the large amount of work put into studying these...

Multiplier method and exact solutions for a density dependent reaction-diffusion equation

Published Online: Jul 01, 2016

Page range: 311 - 320

Received: Mar 05, 2016

Accepted: Jul 01, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00026

Keywords
Lie symmetries, Partial differential equations, Conservation laws, Fisher equation

© 2016 M. Rosa, M. L Gandarias, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Multiplier method and exact solutions for a density dependent reaction-diffusion equation

Published Online: Jul 01, 2016

Page range: 311 - 320

Received: Mar 05, 2016

Accepted: Jul 01, 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00026

KeywordsLie symmetries, Partial differential equations, Conservation laws, Fisher equation

© 2016 M. Rosa, M. L Gandarias, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Lie symmetries, Partial differential equations, Conservation laws, Fisher equation