Dark-bright optical solitary waves and modulation instability analysis with (2 + 1)-dimensional cubic-quintic nonlinear Schrödinger equation

• Published in: Waves in random and complex media Vol. 29; no. 3; pp. 393 - 402
• Main Authors: Inc, Mustafa, Aliyu, Aliyu Isa, Yusuf, Abdullahi, Baleanu, Dumitru
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.07.2019; Taylor & Francis Ltd
• Subjects: Computer simulation; Mathematical models; Modulation; Optical properties; Schrodinger equation; Solitary waves; Stability; Stability analysis
• ISSN: 1745-5030; 1745-5049
• DOI: 10.1080/17455030.2018.1440096

This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrödinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark-bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.