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International Conference on Numerical Analysis and Its Applications

NAA 2004: Numerical Analysis and Its Applications pp 590–597Cite as

Parametrically Driven Dark Solitons: A Numerical Study

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3401))

Abstract

We show that unlike the bright solitons, the parametrically driven kinks of the nonlinear Schrödinger equation are immune from instabilities for all damping and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of kinks and their complexes can stably travel with nonzero velocities. The bistability of the Bloch and Néel walls within the NLS contrasts the properties of these solutions within the Ginzburg-Landau equation, where they cannot stably coexist.

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Author information

Authors and Affiliations

  1. Laboratory for Information Technologies, Joint Institute for Nuclear Research, Dubna, 141980, Russia

    E. V. Zemlyanaya

  2. Department of Applied Mathematics, University of Cape Town, Rondebosch, 7701, South Africa

    I. V. Barashenkov & S. R. Woodford

Authors
  1. E. V. Zemlyanaya
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  2. I. V. Barashenkov
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  3. S. R. Woodford
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Editor information

Editors and Affiliations

  1. Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, P.O. Box, Hong Kong

    Zhilin Li

  2. Department of Mathematics, University of Rousse, 7017, Rousse, Bulgaria

    Lubin Vulkov

  3. Informatics & Mathematical Modeling, Technical University of Denmark, DK-2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2005 Springer-Verlag Berlin Heidelberg

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Zemlyanaya, E.V., Barashenkov, I.V., Woodford, S.R. (2005). Parametrically Driven Dark Solitons: A Numerical Study. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_72

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  • DOI: https://doi.org/10.1007/978-3-540-31852-1_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24937-5

  • Online ISBN: 978-3-540-31852-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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