Soliton and similarity solutions of N=2,4 supersymmetric equations

TL;DR

This paper constructs soliton and similarity solutions for supersymmetric extensions of classical equations like Burgers and KdV, introducing new tau-function representations and virtual solitons with unique interaction properties.

Contribution

It provides novel solutions and tau-function representations for supersymmetric equations, including the concept of virtual solitons with no phase shifts during interactions.

Findings

New soliton and similarity solutions for supersymmetric equations.

Introduction of virtual solitons with no phase shifts.

New tau-function representations in Hirota bilinear formalism.

Abstract

We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the $\tau$-functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.