Symmetry-adapted moving mesh schemes for the nonlinear Schrodinger equation

@article{Budd2001SymmetryadaptedMM,
  title={Symmetry-adapted moving mesh schemes for the nonlinear Schrodinger equation},
  author={Chris J. Budd and V. A. Dorodnitsyn},
  journal={Journal of Physics A},
  year={2001},
  volume={34},
  pages={10387-10400}
}
In this paper we consider symmetry-preserving difference schemes for the nonlinear Schrodinger equation 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… Expand
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