Grassmanian and Bosonic Thirring Models with Jump Defects

TL;DR

This paper explores the integrability of Grassmanian and Bosonic Thirring models with jump defects using Lax formulation and Bäcklund transformations, demonstrating the models' preservation of integrability through explicit transitions.

Contribution

It extends the Bäcklund transformation framework to Bosonic Thirring models with jump defects, confirming integrability via Lax formulation and explicit soliton transitions.

Findings

Bäcklund transformation preserves integrability in Grassmanian models.

Extended Bäcklund transformation verified for Bosonic Thirring model.

Lax formulation confirms integrability with jump defects.

Abstract

In this paper we discuss the Lax formulation of the Grassmanian and Bosonic Thirring models in the presence of jump defects. For the Grassmanian case, the defect is described by B\"acklund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the B\"acklund transformation for the Bosonic Thirring model which is verified by some B\"acklund transitions like Vacuum-One soliton, One soliton - One soliton, One soliton - Two solitons and Two solitons - Two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model.