Optical Solitons with the Complex Ginzburg–Landau Equation with Kudryashov’s Law of Refractive Index

Abstract

In this paper, the optical solitons for the complex Ginzburg–Landau equation with Kudryashov’s law of refractive index are established. An improved modified extended tanh–function technique is used to extract numerous solutions. Bright and dark solitons, as well as singular soliton solutions, are achieved. In addition, as the modulus of ellipticity approaches unity or zero, solutions are formulated in terms of Jacobi’s elliptic functions, which provide solitons and periodic wave solutions.