A Meshfree Splitting Method for Soliton Dynamics in Nonlinear Schrödinger Equations

  • Marco Caliari
  • Alexander Ostermann
  • Stefan Rainer
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 89)


A new method for the numerical simulation of the so-called soliton dynamics arising in a nonlinear Schrödinger 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 one to keep the degrees of freedom almost constant as the semi-classical parameter \(\epsilon \) becomes small. This behavior is confirmed by numerical experiments.


Meshfree discretization Splitting methods Nonlinear Schrödinger equations Soliton dynamics Semi-classical regime 



The work of Stefan Rainer was partially supported by the Tiroler Wissenschaftsfond grant UNI-0404/880.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Marco Caliari
    • 1
  • Alexander Ostermann
    • 2
  • Stefan Rainer
    • 2
  1. 1.Dipartimento di InformaticaUniversità di VeronaVeronaItaly
  2. 2.Institut für MathematikUniversität InnsbruckInnsbruckAustria

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