Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

TL;DR

This paper introduces a new super-Backlund transformation for the N=1 super sinh-Gordon model, proposes a compatible type-II integrable defect, and derives explicit conserved quantities, enhancing understanding of supersymmetric integrable systems.

Contribution

It constructs a novel super-Backlund transformation and develops a consistent type-II defect framework for the supersymmetric sinh-Gordon model, including explicit conserved quantities.

Findings

New super-Backlund transformation for N=1 super sinh-Gordon

Consistent type-II integrable defect proposed

Explicit conserved energy, momentum, supercharges derived

Abstract

A new super-Backlund transformation for the N=1 supersymmetric sinh-Gordon equation is constructed. Based on this construction we propose a type-II integrable defect for the supersymmetric sinh-Gordon model consistent with this new transformation through the Lagrangian formalism. Explicit expressions for the modified conserved energy, momentum and supercharges are also computed. In addition, we show for the model that the type-II defect can also been regarded as a pair of fused defects of a previously introduced type. The explicit derivation of the associated defect matrices is also presented as a necessary condition for the integrability of the model.