On closed-form optical solutions to the nonlinear model with the Kerr law nonlinearity

Abstract

The main contribution of this study is the application of a newly-proposed method to the Ginzburg–Landau equation arising from the propagation of nonlinear waves to obtain new closed-form optical solutions to this equation. By employing a wave transformation, we are able to reduce the nonlinear model to an ordinary differential equation. With the use of this method, a variety of structures are obtained resulting from different combinations of expressions. Also, we present some 2D plots to probe the underlying optical wave properties of the model. It is important to note that the proposed technique is very simple, and straightforward, and can be applied to solve non-linear partial differential equations. All symbolic programs have been coded in Mathematica.

Keywords

• mGERFM
• The Jacobi elliptical finder method
• Closed-form
• Propagation
• Nonlinear waves