Solitons in Optical Metamaterials with Trial Solution Approach and Bäcklund Transform of Riccati Equation

This paper obtains soliton solutions in optical metamaterials. There are a couple of integration techniques that are applied to the nonlinear Schrödinger’s equation, with full nonlinearity, that serves as the governing model. These are trial solution approach and application of Bäcklund transform to Riccati equation. There are four types of nonlinear media that are studied in this paper. They are Kerr law that is also referred to as cubic law, power law, parabolic law occasionally referred to as cubic-quintic law and finally dual-power law nonlinearity. Bright, dark and singular soliton solutions are obtained in optical metamaterials with the aid of the two algorithms. As a byproduct of these two approaches, singular periodic solutions and plane wave solutions are also listed although these are not utilized in optical metamaterials. There are several constraint conditions that naturally fall out from the solution structure. These conditions guarantee the existence of these variety of solutions.