Article ID Journal Published Year Pages File Type
759346 Communications in Nonlinear Science and Numerical Simulation 2010 10 Pages PDF
Abstract

We search for traveling-wave solutions of two classes of equations:(I.)Class of reaction-diffusion equations∂Q∂t+dDdQ∂Q∂x2+D(Q)∂2Q∂x2+F(Q)=0(II.)Class of reaction-telegraph equations∂Q∂t-α∂2Q∂t2-β∂2Q∂x2-γdFdQ∂Q∂t-F(Q)=0Above α, β, γ are parameters and D and F depend on the population density Q. We obtain such solutions by the modified method of simplest equation for the cases when the simplest equation is the equation of Bernoulli or the equation of Riccati. On the basis of the appropriate ansatz the PDEs are reduced to nonlinear algebraic systems of relationships among the parameters of the equations and the parameters of the solution. By means of these systems we obtain numerous solutions for PDEs belonging to the investigated classes of equations.

Related Topics
Physical Sciences and Engineering Engineering Mechanical Engineering
Authors
, ,