Unraveling hidden hierarchies and dual structures in an integrable field model

TL;DR

This paper explores the hidden hierarchical and dual structures in an integrable field model, specifically the nonlinear Schrödinger equation, demonstrating complete integrability through a novel Yang-Baxter equation at both classical and quantum levels.

Contribution

It introduces a new Yang-Baxter equation framework that reveals hidden hierarchies and dual structures in integrable field theories, with exact solutions for the nonlinear Schrödinger equation.

Findings

Unveiled hidden hierarchies and dual structures in the nonlinear Schrödinger equation.

Established complete integrability via a novel classical and quantum Yang-Baxter equation.

Provided exact solutions demonstrating the integrability and dual charge contributions.

Abstract

An integrable field theory, due to path-independence on the space-time plane, should yield together with an infinite set of independent conserved charges also similar dual charges determining the boundary and defect contributions. On the example of the nonlinear Schroedinger equation we unravel hidden hierarchies and dual structures and show the complete integrability through a novel Yang-Baxter equation at the classical and quantum level with exact solution.