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

Resumen

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. It is known that conservation laws play a significant role in the solution process of an equation or a system of differential equations. Although not all of the conservation laws of partial differential equations (PDEs) may have physical interpretation they are essential in studying the integrability of the PDEs. In, 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.