Integrablility of a Classical $N= 2$ Super Sinh-Gordon Model with Jump Defects

TL;DR

This paper demonstrates the integrability of the classical N=2 super sinh-Gordon model with jump defects by constructing conserved quantities, supersymmetric transformations, and soliton solutions, confirming its infinite conserved charges.

Contribution

It introduces a Lagrangian formalism with border functions, constructs conserved quantities, and proves integrability via a Lax formulation based on affine super Lie algebra.

Findings

Existence of infinite conserved charges.

Construction of supersymmetric Backlund transformation.

Explicit one-soliton solution obtained.

Abstract

The Lagrangian formalism for the N=2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is given and an one-soliton solution is obtained. The Lax formulation based on the affine super Lie algebra $sl(2,2)$ within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.