Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories

Abstract

Based on the recent formulation of a general scheme to construct boundary Lax pairs,we develop this systematic construction for the $A_n^{(1)}$ affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sine-Gordon ($A_1^{(1)}$) and the $A_2^{(1)}$ models. The $A_2^{(1)}$ Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.

30 pages, Latex. Typos corrected, clarifications added. Version to appear in NBP

References in corpus (4)

• The generalized non-linear Schrodinger model on the interval
• Integrable boundary conditions and modified Lax equations
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers

Cited by in corpus (7)

• Set-theoretical reflection equation: Classification of reflection maps
• The sine-Gordon model with integrable defects revisited
• Sigma models in the presence of dynamical point-like defects
• Jumps and twists in affine Toda field theories
• The sine-Gordon model in the presence of defects
• Lax pair formulation in the simultaneous presence of boundaries and defects
• Scattering matrices in the sl(3) twisted Yangian