A novel approach to construct optical solitons solutions of complex Ginzburg–Landau equation with five distinct forms of nonlinearities

This paper presents a recently introduced innovative approach for analyzing closed-form solutions of nonlinear partial differential equations. While various methods exist for deriving closed-form solutions to many nonlinear evolution equations, additional solutions are still needed to study the various dynamics of physical systems governed by nonlinear partial differential equations. Initially, we give general procedure of the Cham technique for solving nonlinear partial differential equations that yields eight kinds of solutions. This technique is applied to the complex Ginzburg–Landau equation, incorporating five different types of nonlinearities: Kerr law, cubic–quintic law, polynomial nonlinearity, quadratic–cubic law, and parabolic-nonlocal law. With the aid of the proposed strategy, we can obtain a wide array of optical solitons, including bright, breather, kink, periodic, and cusp-shaped solitons, under specific parameter conditions.