Numerical approaches to solving a nonlinear system of Schrodinger equations for wave propagation in an optical fiber

摘要

The paper discusses approaches to the numerical integration of the second-kind Manakov equation system. Emphasis is placed on the transition from writing equations in dimensional quantities to equations in dimensionless units. A combined explicit/implicit finite-difference integration scheme based on the implicit Crank - Nicolson finite-difference scheme is proposed and substantiated, which allows integrating a nonlinear system of equations with a choice of nonlinear term at the previous integration step. An algorithm for levelling the disadvantage associated with the definition of the nonlinear term from the previous integration step is proposed. The approach of automatic selection of the integration step, which reduces the total number of integration steps while maintaining the required accuracy of the approximate solution, is substantiated. Examples of the calculation results for some values of the disturbance propagation are given. The limitations imposed by the computing scheme on the length of the integrable fiber section are described, and approaches, that eliminate these limitations without the need to increase arrays dimensions, are proposed. Requirements for initial boundary conditions are discussed.