*American Journal of Applied Mathematics and Statistics*.

**2018**, 6(6), 244-252

DOI: 10.12691/ajams-6-6-5

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

**Anika Tashin Khan**^{1} and **Hasibun Naher**^{1, }

^{1}Department of Mathematics and Natural Sciences, BRAC University, 66 Mohakhali, Dhaka 1212, Bangladesh

**Cite this paper:**

Anika Tashin Khan and Hasibun Naher. Solitons and Periodic Solutions of the Fisher Equation with Nonlinear Ordinary Differential Equation as Auxiliary Equation. *American Journal of Applied Mathematics and Statistics*. 2018; 6(6):244-252. doi: 10.12691/ajams-6-6-5

### Abstract

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.**Keywords:**New extension of the generalized and improved (G’/G)-expansion method Nonlinear evolution equation (NLEE) Fisher Equation Wave solutions Nonlinear partial differential equation (NLPDE)

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