In this paper, different types of soliton solutions of the modified equal width wave (MEW) equation with beta time derivative are obtained by implementing the two different methods named as: extended Jacobi's elliptic expansion function method and Kudryashov method. The dark, bright, singular and other solitons are achieved. The obtained soliton solutions are verified through MATHEMATICA. At the end, the results are also explained through graphs. These soliton solutions suggest that these two methods are effective, straight forward and reliable as compare to other methods. The obtained results can be used in describing the substantial understanding of the studious structures as well as others related non-linear physical structures.
