Classical integrability of the O(N) nonlinear Sigma model on a half-line

TL;DR

This paper investigates the classical integrability of the O(N) nonlinear sigma model on a half-line, demonstrating the existence of infinite conserved charges under free boundary conditions and exploring additional boundary conditions for N=3.

Contribution

It establishes the presence of an infinite number of conserved charges for the model with free boundary conditions and discusses alternative boundary conditions for N=3.

Findings

Infinite conserved charges exist under free boundary conditions.

Classical integrability is confirmed for the model on a half-line.

Additional boundary conditions are considered for N=3.

Abstract

The classical integrability the O(N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N=3 other possible boundary conditions are considered briefly.