Symmetry-adapted moving mesh schemes for the nonlinear Schroedinger equation

In this paper we consider symmetry-preserving difference schemes for the nonlinear Schroedinger equation i(∂u)/∂r+(∂2u)/∂r2+(n-∂u)/r(∂u)/∂r+u vertical bar u vertical bar2=0 where n is the number of space dimensions. This equation describes one-dimensional waves in n space dimensions in many physical situations, including phenomena in plasma physics and nonlinear optics. We will consider the nonintegrable case n≥2 for which the equation admits solutions that blow up in a finite time, and construct discretizations based upon moving mesh schemes that have the same Lie group properties and Lagrangian structures as the continuous counterpart. (author)