The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
نویسندگان
چکیده
The “interaction picture” (IP) method is a very promising alternative to Split-Step methods for solving certain type of partial differential equations such as the nonlinear Schrödinger equation involved in the simulation of wave propagation in optical fibers. The method exhibits interesting convergence properties and is likely to provide more accurate numerical results than cost comparable Split-Step methods such as the Symmetric Split-Step method. In this work we investigate in detail the numerical properties of the IP method and carry out a precise comparison between the IP method and the Symmetric Split-Step method.
منابع مشابه
He’s Semi-Inverse Method and Ansatz Approach to look for Topological and Non-Topological Solutions Generalized Nonlinear Schrödinger Equation
This paper obtains the exact 1-soliton solutions to generalized nonlinear Schrödinger equation. Nonlinear Schrödinger equation has been widely applied in many branches of nonlinear sciences such as nonlinear optics, nonlinear optical fibers and quantum mechanics. So, finding exact solutions of such equations are very helpful in the theories and numerical studies. In this paper, the He’s semi-in...
متن کاملThe smoothed particle hydrodynamics method for solving generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system
A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...
متن کاملInverse scattering approach to coupled higher order nonlinear Schrödinger equation and N -soliton solutions
A generalized inverse scattering method has been applied to the linear problem associated with the coupled higher order nonlinear schrödinger equation to obtain it’s N -soliton solution. An infinite number of conserved quantities have been obtained by solving a set of coupled Riccati equations. It has been shown that the coupled system admits two different class of solutions, characterised by t...
متن کاملVariational homotopy perturbation method for solving the generalized time-space fractional Schrödinger equation
We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method. We use this method for solving Generalized Time-space Fractional Schrödinger equation. The fractional derivative is described in Caputo sense. The proposed scheme finds the solution without any discritization, ...
متن کاملComparison of adaptive step-size control strategies for solving the Generalised Non-Linear Schrodinger Equation in optics by the Interaction Picture method
This report is devoted to the study and to the comparison of methods for estimation of the local error and for adaptive step-size control when solving the generalised nonlinear Schrodinger equation (GNLSE) in optics by the Interaction Picture (IP) method or by the Symmetric Split-Step (S3F) method. Namely, we propose and study the use of an embedded Runge-Kutta method to solve the nonlinear pro...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013