The aim of this project is to develop fast methods for the solution of nonlinear Schrödinger type equations in fiber optics. Using the method of lines we have to solve a stiff system of ordinary differential equations where the eigenvalues of the Jacobian are close to the imaginary axis. This is usually done by a Split Step method. Here we consider the extrapolation of Split Step methods with adaptive order and step size control. For more complicated nonlinearities, in particular stimulated Raman scattering, Split Step methods are less efficient since symmetry is either destroyed or requires much additional effort. In this case we use implicit Runge Kutta formulas of Gauss type. The key point for the efficient implementation of these methods is that the system of nonlinear algebraic equations can be solved without setting up the Jacobian

Results

Split Step Methods tested with solitons and WDM signals WDM test signal with 2 channels.

Comparison of various methods for the solution of the nonlinear Schrödinger equation.