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This article is cited in 9 scientific papers (total in 9 papers)
Hirota's virtual multisoliton solutions of $N=2$ supersymmetric Korteweg–de Vries equations
A. V. Kiseleva, V. Hussinb a University Utrecht, Mathematical Institute
b Université de Montréal, Département de Mathématiques et de
Statistique
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 $t\ll0$, 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 $\tau$-function as time increases.
Keywords:
Hirota's soliton, $N=2$ supersymmetric KdV, Krasil'shchik–Kersten system, phase shift, spontaneous decay.
Citation:
A. V. Kiselev, V. Hussin, “Hirota's virtual multisoliton solutions of $N=2$ supersymmetric Korteweg–de Vries equations”, TMF, 159:3 (2009), 490–501; Theoret. and Math. Phys., 159:3 (2009), 833–841
Linking options:
https://www.mathnet.ru/eng/tmf6367https://doi.org/10.4213/tmf6367 https://www.mathnet.ru/eng/tmf/v159/i3/p490
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Abstract page: | 402 | Full-text PDF : | 211 | References: | 55 | First page: | 25 |
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