Hirota’s virtual multi-soliton solutions of N = 2 supersymmetric KdV equations

We prove that Mathieu’s N = 2 supersymmetric Korteweg–de Vries equations with a = 1 or 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 τ -function as the time grows.