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

TL;DR

This paper proves the existence of Hirota's n-supersoliton solutions for N=2 supersymmetric KdV equations, revealing unique interactions like no phase shifts and spontaneous decay into different solitonic states, highlighting their integrability.

Contribution

It demonstrates the existence of supersoliton solutions with unique interaction properties in N=2 super-KdV systems, including virtual solitons and spontaneous decay phenomena.

Findings

Supersoliton solutions admit no phase shifts during interaction.

Initial profiles can spontaneously decay and transform into different solitons.

Virtual solitons become manifest over time through the tau-function.

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.