Hirota's virtual multi-soliton solutions of N=2 supersymmetric Korteweg-de Vries equations

Abstract

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.

Proc. 5th International Workshop `Nonlinear Physics: Theory and Experiment' (June 12-21, 2008; Gallipoli, Italy), 11 pages

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Cited by in corpus (5)

• Classical and SUSY solutions of the Boiti-Leon-Manna-Pempinelli equation
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• Gardner's deformations of the graded Korteweg-de Vries equations revisited
• A novel Hirota bilinear approach to $N=2$ supersymmetric equations
• On the (non)removability of spectral parameters in $Z_2$-graded zero-curvature representations and its applications