Geodesic
Hirota's virtual multisoliton solutions of $N=2$ supersymmetric Korteweg--de Vries equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 490-501

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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.
Mots-clés : Hirota's soliton
Keywords: $N=2$ supersymmetric KdV, Krasil'shchik–Kersten system, phase shift, spontaneous decay. 
@article{TMF_2009_159_3_a14,
     author = {A. V. Kiselev and V. Hussin},
     title = {Hirota's virtual multisoliton solutions of $N=2$ supersymmetric {Korteweg--de} {Vries} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {490--501},
     publisher = {mathdoc},
     volume = {159},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a14/}
}
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A. V. Kiselev; V. Hussin. Hirota's virtual multisoliton solutions of $N=2$ supersymmetric Korteweg--de Vries equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 3, pp. 490-501. http://geodesic.mathdoc.fr/item/TMF_2009_159_3_a14/