Exact Optical Solitons for Generalized Kudryashov's Equation by Lie Symmetry Method

In this article, we use Lie point symmetry analysis to extract some new optical soliton solutions for the generalized Kudryashov's equation (GKE) with an arbitrary power nonlinearity. Using a traveling wave transformation, the GKE is transformed into a nonlinear second order ordinary differential equation (ODE). Using Lie point symmetry analysis, the nonlinear second-order ODE is reduced to a first-order ODE. This first-order ODE is solved in two cases to retrieve some new bright, dark, and kink soliton solutions of the GKE. These soliton solutions for the GKE are obtained here for the first time.