Abstract
This article aims to identify solitary wave solutions to a nonlinear Kudryashov's equation utilizing an exponential rational function method and Painleve approach. This model is used to interpret the propagation of modulated envelope signals which disseminate with some group velocity. These two different methods are applied to build analytical solutions of the model that are relatively new and effective to solve the nonlinear evolution equation. Hyperbolic wave function and kink solitons are two types of traveling wave solutions that can be obtained using these techniques. For the existence of these solitons, constraint conditions on the parameters have also been listed. Graphical illustrations have also been given to understand the physical significance of the proposed model. In the end stability analysis of the obtained solution is carried out for depicting the importance of the model.