Speaker
Paul Bergold
Description
We present a novel numerical method for solving nonlinear Schrödinger (NLS) equations with time-dependent potentials on the real line. The spatial discretization employs a Hermite spectral decomposition, providing analytical expressions for the evolution of basis functions under the free Schrödinger operator. A linearization approach for solutions to the underlying NLS equation with time-dependent potential leads to a second-order Strang type time-splitting scheme, derived by combining the variation-of-constants formula with quadrature rules. Numerical experiments on the Gross—Pitaevskii equation, widely used in quantum physics to describe Bose—Einstein condensates, are presented to support the theoretical results.
