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

Arnous, Ahmed H.; Moraru, Luminita

doi:10.3390/math10193456

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Article

22 September 2022

13 Pages

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

and

Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, Cairo 11837, Egypt

Department of Chemistry, Physics and Environment, Faculty of Sciences and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania

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Mathematics2022, 10(19), 3456;https://doi.org/10.3390/math10193456

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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.

Keywords:

optical solitons; Kudryashov; Ginzburg–Landau equation

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