Strang Splitting Methods for a quasilinear Schrödinger equation - Convergence, Instability and Dynamics

Abstract: We study the Strang splitting scheme for quasilinear Schr\"odinger equations. We establish the convergence of the scheme for solutions with small initial data. We analyze the linear instability of the numerical scheme, which explains the numerical blow-up of large data solutions and connects to analytical breakdown of regularity of solutions to quasilinear Schr\"odinger equations. Numerical tests are performed for a modified version of the superfluid thin film equation.