Classical Integrable Super sinh-Gordon equation with defects

TL;DR

This paper explores the integrability of the N=1 super sinh-Gordon model with defects, constructing conserved quantities and soliton solutions, and demonstrating the model's infinite conserved charges through Lax formalism.

Contribution

It introduces a Lagrangian and Bäcklund transformation framework for the super sinh-Gordon model with defects, establishing its integrability and explicit soliton solutions.

Findings

Modified conserved momentum and energy are derived.

Explicit Bäcklund soliton solutions are presented.

The model's integrability is confirmed via Lax formulation.

Abstract

The introduction of defects is discussed under the Lagrangian formalism and Backlund transformations for the N=1 super sinh-Gordon model. Modified conserved momentum and energy are constructed for this case. Some explicit examples of different Backlund solitons solutions are discussed. The Lax formulation 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