The Radhakrishnan-Kundu-Lakshmanan equation with arbitrary refractive index and its exact solutions

The Radhakrishnan-Kundu-Lakshmanan equation is studied with arbitrary refractive index. The partial differential equation is not integrable and we look for exact solutions using the traveling wave reduction. The overdetermined system of equations is presented for the packet wave envelope. Two compatibility conditions for existence of exact solutions to the overdetermined system of equations are used to construct solutions of nonlinear ordinary differential equations. Exact solutions in the form of periodic and solitary waves of the generalized Radhakrishnan-Kundu-Lakshmannan equation are given.

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In this study, the Radhakrishnan-Kundu-Lakshmanan equation is examined with arbitrary refractive index, and exact solutions are sought using the traveling wave reduction technique. An overdetermined system of equations is introduced for the packet wave envelope, and two compatibility conditions are used to construct solutions of nonlinear ordinary differential equations. Exact solutions in the form of periodic and solitary waves of the generalized Radhakrishnan-Kundu-Lakshmannan equation are provided.