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

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Cited by in corpus (15)

• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• From Hamiltonian to zero curvature formulation for classical integrable boundary conditions
• Non-commutative NLS-type hierarchies: dressing & solutions
• New integrable boundary conditions for the Ablowitz-Ladik model: from Hamiltonian formalism to nonlinear mirror image method
• Time-like boundary conditions in the NLS model
• Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary
• A Dual Construction of the Isotropic Landau-Lifshitz Model
• Generalized Landau-Lifshitz models on the interval
• Boundary Lax pairs from non-ultra local Poisson algebras
• Discretizations of the generalized AKNS scheme
• An algebraic approach to discrete time integrability
• Lax pair formulation in the simultaneous presence of boundaries and defects
• Selected Topics in Classical Integrability
• Systematic derivation of boundary Lax pairs
• Hydrodynamic type integrable equations on a segment and a half-line