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.

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

An Approximate Solution of Blasius Equation by using HPM Method

Abstract In this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Soliton solution and bifurcation analysis of the Zakharov–Kuznetsov–Benjamin–Bona–Mahoney equation with power law nonlinearity

Approximate analytical solutions of fractional gas dynamic equations

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Explicit Solution of Nonlinear ZK-BBM Wave Equation Using Exp-Function Method

Application of Homotopy Analysis Method and Variational Iteration Method for Shock Wave Equation

A special form of generalized nonlinear Benjamin–Bona–Mahony–Burgers (BBMB) equations is investigated in an analytical solution. The analysis is based on the implementation a new method, called Exp-function method. The obtained results from the proposed approximate solution has been compared and verified with those obtained by the exact solution. It shows that the numerical results of these methods are the same; while Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear partial differential equations of engineering problems in the terms of accuracy and efficiency.

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J. Mahmoudi

Papers

Explicit Solution of Nonlinear ZK-BBM Wave Equation Using Exp-Function Method

Application of Homotopy Analysis Method and Variational Iteration Method for Shock Wave Equation

Solitary and Periodic Solutions of BBMB Equation via Exp-Function Method

On the Non-Linear Deformation of Elastic Beams in an Analytic Solution

198 the effect of sericin on underactive bladder model following lumbar canal stenosis