Integrable boundary conditions and modified Lax equations

Abstract

We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding transfer matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix and the boundary matrix.

27 pages Latex. References added and typos corrected

References in corpus (3)

• The generalized non-linear Schrodinger model on the interval
• Integrable Models From Twisted Half Loop Algebras
• (Quantum) twisted Yangians: symmetry, Baxterisation and centralizers

Cited by in corpus (1)

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