Classically integrable boundary conditions for affine Toda field theories

TL;DR

This paper investigates boundary conditions that preserve classical integrability in affine Toda field theories, developing new methods to identify and classify such conditions.

Contribution

It introduces a generalized Lax pair approach and provides a comprehensive set of conjectures for permissible boundary conditions in affine Toda theories.

Findings

Constructed conserved quantities explicitly for boundary conditions.

Developed a generalized Lax pair framework.

Proposed conjectures for boundary conditions in all affine Toda models.

Abstract

Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory.