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Numerical Study of Travelling Multi-soliton Complexes in the Ac-Driven NLS Equation

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Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

Travelling solitons of the undamped, externally driven nonlinear Schrödinger equation (NLS) are investigated by the numerical solution of the reduced ordinary differential equation and the corresponding linearized eigenvalue problem. This numerical approach is complemented by direct numerical simulations of the partial differential NLS equation. We show that in the small driving case, travelling solitons can form stably travelling bound states.

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References

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Author information

Authors and Affiliations

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

    Elena Zemlyanaya

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

    Nora Alexeeva

Authors
  1. Elena Zemlyanaya
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  2. Nora Alexeeva
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Zemlyanaya, E., Alexeeva, N. (2013). Numerical Study of Travelling Multi-soliton Complexes in the Ac-Driven NLS Equation. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_63

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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