Solitons and Periodic Solutions of the Fisher Equation with Nonlinear Ordinary Differential Equation as Auxiliary Equation

In this article the new extension of the generalized and improved (G’/G)-expansion method has been used to generate many new and abundant solitons and periodic solutions, where the nonlinear ordinary differential equation has been used as an auxiliary equation, involving many new and real parameters. We choose the Fisher Equation in order to explain the advantages and effectives of this method. The illustrated results belongs to hyperbolic functions, trigonometric functions and rational functional forms which show that the implemented method is highly effective for investigating nonlinear evolution equations in mathematical physics and engineering science.

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