Towards a Unified Method for Exact Solutions of Evolution Equations. An Application to Reaction Diffusion Equations with Finite Memory Transport

Abstract

We present a brief report on the different methods for finding exact solutions of nonlinear evolution equations. Explicit exact traveling wave solutions are the most amenable besides implicit and parametric ones. It is shown that most of methods that exist in the literature are equivalent to the "generalized mapping method" that unifies them. By using this method a class of formal exact solutions for reaction diffusion equations with finite memory transport is obtained. Attention is focused to the finite-memory-transport-Fisher and Nagumo equations.

Multi-soliton rational solutions for some nonlinear evolution equations

“…The fundamental rules and objectives of the uni ed method are used here (for details see [19]). The only distinction is that the main aim in [19] is to search for a single traveling wave solution, namely…”

“…The only distinction is that the main aim in [19] is to search for a single traveling wave solution, namely…”

“…By using the uni ed method [19], we obtain solutions in the form; (i) Polynomial function solutions (ii) Rational function solutions In this paper, we con ne ourselves to nd rational function solutions.…”

“…It is worth to be noticing that, n and k are determined from the balance equation by the criteria given in [19][20][21]. Also, a second condition (the consistency condition), which asserts that the constants in Equations (4) and (5) could be consistently determined, is used.…”

On The Features Solitary Wave Solutions for the DoubleStructures Model of DNA

“…In this work, we have to find the traveling wave solutions TWS of equation (9) by using the unified method UM [33]. The outline of this method are introduced as follows:…”