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This paper aims to show that the variational iteration method (VIM) and the homotopy perturbation method (HPM) are powerful and suitable methods to solve the Fornberg‐Whitham equation.

Using HPM the explicit exact solution is calculated in the form of a quickly convergent series with easily computable components. Also, by using VIM the analytical results of this equation have been obtained in terms of convergent series with easily computable components.

Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of high accuracy.

Also the results show that the introduced methods are efficient tools for solving the nonlinear partial differential equations.

The purpose of this paper is to use He's Exp‐function method (EFM) to construct solitary and soliton solutions of the nonlinear evolution equation.

This technique is straightforward and simple to use and is a powerful method to overcome some difficulties in the nonlinear problems.

This method is developed for searching exact traveling wave solutions of the nonlinear partial differential equations. The EFM presents a wider applicability for handling nonlinear wave equations.

The paper shows that EFM, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations. Application of EFM to Fitzhugh‐Nagumo equation illustrates its effectiveness.