Bright and Singular Optical Solitons in Nonlinear Negative-Index Materials with Quadratic–Cubic Nonlinearity

• Published in: Arabian journal for science and engineering (2011) 2021-06, Vol.46 (6), p.5977-5991
• Main Authors: Rezazadeh, Hadi, Abazari, Reza, Justin, Mibaile, Bekir, Ahmet, Korkmaz, Alper
• Format: Article
• Language: English
• Subjects: Differential equations; Engineering; Humanities and Social Sciences; Metamaterials; multidisciplinary; Multiplication; Nonlinearity; Optical properties; Ordinary differential equations; Research Article-Physics; Schrodinger equation; Science; Solitary waves
• ISSN: 2193-567X; 1319-8025; 2191-4281
• DOI: 10.1007/s13369-020-05194-y

Generally, metamaterials are any material with a special properties that are not in nature. Among them, the optical metamaterial is a type of electromagnetic metamaterial, that interacts with light or visible wavelengths. The mathematical modeling of this interaction is usually introduce by perturbed Schrödinger equation. The aim of this paper is to study the perturbed Schrödinger equation model of optical metamaterials for obtaining their solitary wave solutions. To obtain the solitary wave solutions of governing equation, we firstly reduced the equation to an ordinary differential equation (ODE), then multiplication of this equation with the derivative of the unknown function leads to a well known ODE. Secondly, integrating this resultant equation for some particular choices of constant coefficients gives many solutions in different classes. Many of these solutions are generalized forms of the solutions reported in the literature. Elliptic and triangular solutions are constructed in various forms besides bright and singular type soliton solutions.