The improved F-expansion method with Riccati equation and its applications in mathematical physics

The improved F-expansion method combined with Riccati equation is one of the most effective analytical methods in finding the exact traveling wave solutions to non-linear evolution equations in mathematical physics. In this article, this method is implemented to investigate new exact solutions to the Drinfel’d–Sokolov–Wilson (DSW) equation and the Burgers equation. The performance of this method is reliable, direct, and simple to execute compared to other existing methods. The obtained solutions in this work are imperative and significant for the explanation of some practical physical phenomena