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.

arXiv comment30 pages, Latex. Typos corrected, clarifications added. Version to appear in NBP

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Cited by in corpus (12)

• Liouville integrable defects: the non-linear Schrodinger paradigm
• 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
• Defects in the discrete non-linear Schrodinger model
• Generalized q-Onsager algebras and boundary affine Toda field theories
• Classical impurities associated to high rank algebras
• Jumps and twists in affine Toda field theories
• Boundary Lax pairs from non-ultra local Poisson algebras
• Lax pair formulation in the simultaneous presence of boundaries and defects
• The sine-Gordon model in the presence of defects
• Scattering matrices in the sl(3) twisted Yangian