Time-integration methods for a dispersion-managed nonlinear Schrödinger equation

Modeling dispersion-managed optical fibers leads to a nonlinear Schrödinger equation where the linear part is multiplied by a rapidly changing piecewise constant coefficient function. Typically, the occurring oscillations of the solution and the discontinuous coefficients impose severe problems for traditional time-integrators. In this thesis, we present and analyze tailor-made numerical methods for this equation which attain a desired accuracy with significantly larger step-sizes than traditional methods. The construction of the methods is based on a favorable transformation of problem and the explicit computation of certain integrals over highly oscillatory phases. In the error analysis, we deviate from the classical concept “stability and consistency yield convergence”. Instead, we utilize recursion formulas for the global error to exploit cancellation effects of various oscillatory error terms allowing us to prove higher accuracy for special step-sizes.