Optical solitons and modulation instability analysis with (3 + 1)-dimensional nonlinear Shrödinger equation

• Published in: Superlattices and microstructures Vol. 112; pp. 296 - 302
• Main Authors: Inc, Mustafa, Aliyu, Aliyu Isa, Yusuf, Abdullahi, Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2017
• Subjects: Complex envelope function ansatz; Optical soliton; Solitary wave ansatz with Jaccobi elliptic function; Stability analysis; Complex envelope function ansatz; Stability analysis; Solitary wave ansatz with Jaccobi elliptic function; Optical soliton
• ISSN: 0749-6036; 1096-3677
• DOI: 10.1016/j.spmi.2017.09.038

This paper addresses the (3 + 1)-dimensional nonlinear Shrödinger equation (NLSE) that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the solitary wave ansatz with Jaccobi elliptic function methods, we present the exact dark, bright and dark-bright or combined optical solitons to the model. The intensity as well as the nonlinear phase shift of the solitons are reported. The modulation instability aspects are discussed using the concept of linear stability analysis. The MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. •The (3 + 1)-dimensional nonlinear Shrödinger's equation is studied.•Optical solitons are constructed using two integration schemes.•The modulation instability aspects are discussed using the concept of linear stability analysis.•Some figures for the obtained solutions are presented.