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.