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Hirota’s virtual multisoliton solutions of N=2 supersymmetric Korteweg-de Vries equations

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Abstract

We prove that for a = 1 or a = 4, the N=2 supersymmetric Korteweg-de Vries (super-KdV) equations obtained by Mathieu admit Hirota’s n-supersoliton solutions, whose nonlinear interaction does not produce any phase shifts. For initial profiles that cannot be distinguished from a one-soliton solution at times t ≪ 0, we reveal the possibility of a spontaneous decay and transformation into a solitonic solution with a different wave number within a finite time. This paradoxical effect is realized by the completely integrable N=2 super-KdV systems if the initial soliton is loaded with other solitons that are virtual and become manifest through the τ-function as time increases.

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Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

    A. V. Kiselev

  2. Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France

    A. V. Kiselev

  3. Département de Mathématiques et de Statistique, Université de Montréal, Montreal, Quebec, Canada

    V. Hussin

Authors
  1. A. V. Kiselev
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  2. V. Hussin
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Correspondence to A. V. Kiselev.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 490–501, June, 2009.

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Kiselev, A.V., Hussin, V. Hirota’s virtual multisoliton solutions of N=2 supersymmetric Korteweg-de Vries equations. Theor Math Phys 159, 833–841 (2009). https://doi.org/10.1007/s11232-009-0071-x

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  • DOI: https://doi.org/10.1007/s11232-009-0071-x

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