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A Meshfree Splitting Method for Soliton Dynamics in Nonlinear Schrödinger Equations

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Meshfree Methods for Partial Differential Equations VI

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 89))

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Verona, Verona, Italy

    Marco Caliari

  2. Institut für Mathematik, Universität Innsbruck, Innsbruck, Austria

    Alexander Ostermann & Stefan Rainer

Authors
  1. Marco Caliari
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  2. Alexander Ostermann
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  3. Stefan Rainer
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Corresponding author

Correspondence to Stefan Rainer .

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Editors and Affiliations

  1. , Institut für Numerische Simulation, Universität Bonn, Wegelerstr. 6, City, 53115, Germany

    Michael Griebel

  2. Institut für Parallele, und Verteilte Systeme, Universität Stuttgart, Universitätsstraße 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Caliari, M., Ostermann, A., Rainer, S. (2013). A Meshfree Splitting Method for Soliton Dynamics in Nonlinear Schrödinger Equations. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations VI. Lecture Notes in Computational Science and Engineering, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32979-1_8

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