Some New Optical Solitons of the Generalized Radhakrishnan–Kundu–Lakshmanan Equations with Powers of Nonlinearity

In this paper, the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are studied, which is one of the important mathematical models in nonlinear optics. Using the complex envelope traveling wave solution, the new generalized Radhakrishnan–Kundu–Lakshmanan equations are transformed into the nonlinear systems of ordinary differential equations. Under certain constraint conditions, the obtained equations are transformed into a special nonlinear equation. With the help of the solution of this nonlinear equation, some new optical solutions of the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are obtained, which include the solitary wave, singular soliton, periodic soliton, singular-periodic soliton, and exponential-type soliton. By numerical simulation, the corresponding graphs of the optical soliton solution of the new generalized Radhakrishnan–Kundu–Lakshmanan equations are given under the given fixed parameter values, which include the 3D graphics of the module and the 3D graphics of the imaginary part. By analyzing the 2D graphics of the module changing with n, the amplitude of the wave is symmetrical or asymmetrical.