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Oscillating solitons of the driven, damped nonlinear SchrÖdinger equation

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Abstract

We obtain time-periodic solitons of the parametrically driven, damped nonlinear Schrödinger equation as solutions of the boundary value problem on a two-dimensional domain. We classify the stability and bifurcations of singly and doubly periodic solutions.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

    E. V. Zemlyanaya

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

    N. V. Alexeeva

Authors
  1. E. V. Zemlyanaya
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  2. N. V. Alexeeva
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Correspondence to E. V. Zemlyanaya.

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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 536–544, June, 2009.

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Zemlyanaya, E.V., Alexeeva, N.V. Oscillating solitons of the driven, damped nonlinear SchrÖdinger equation. Theor Math Phys 159, 870–876 (2009). https://doi.org/10.1007/s11232-009-0075-6

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  • DOI: https://doi.org/10.1007/s11232-009-0075-6

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