A Meshfree Splitting Method for Soliton Dynamics in Nonlinear Schroedinger Equations

A new method for the numerical simulation of the so-called solitondynamics arising in a nonlinear Schroedinger equation in the semi-classical regime is proposed. For the time discretization a classical fourth-order splitting method is used. For the spatial discretization, however, a meshfree method is employed in contrast to the usual choice of (pseudo) spectral methods. This approach allows to keep the degrees of freedom almost constant as the semi-classical parameter becomes small. This behavior is confirmed by numerical experiments.