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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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