Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-10-06
Theoret.Math.Phys. (2009) V.159, No.3, 832--840.
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Proc. 5th International Workshop `Nonlinear Physics: Theory and Experiment' (June 12-21, 2008; Gallipoli, Italy), 11 pages
Scientific paper
We prove that Mathieu's N=2 supersymmetric Korteweg-de Vries equations with a=1 or a=4 admit Hirota's n-supersoliton solutions, whose nonlinear interaction does not produce any phase shifts. For initial profiles that can not be distinguished from a one-soliton solution at times t<<0, we reveal the possibility of a spontaneous decay and, within a finite time, transformation into a solitonic solution with a different wave number. This paradoxal effect is realized by the completely integrable N=2 super-KdV systems, whenever the initial soliton is loaded with other solitons that are virtual and become manifest through the tau-function as the time grows. Key words and phrases: Hirota's solitons, N=2 supersymmetric KdV, Krasil'shchik-Kersten system, phase shift, spontaneous decay.
Hussin Veronique
Kiselev Arthemy V.
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