Integrable boundary conditions and modified Lax equations
نویسندگان
چکیده
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. [email protected] [email protected]
منابع مشابه
Lax pair formulation for a small-polaron chain with integrable boundaries
Recently, there has been renewed interest in integrable boundary systems [1, 2] due to their connection to the Kondo problem [3] and boundary conformal field theory [4] in low-dimensional quantum many-body systems. Sklyanin [5] proposed a systematic approach to construct and solve integrable quantum spin systems with open boundary conditions (BC). Central to his method is the introduction of th...
متن کاملGeneralized Landau-Lifshitz models on the interval
We study the classical generalized gln Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl2 L-L model. Novel expressions of the modified Lax pairs associated to the integrals of motion are also extracted. The relevant equations of mo...
متن کاملLax pair formulation in the simultaneous presence of boundaries and defects
Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equations of motion on the defect point are accordingl...
متن کاملOn Bäcklund transformations and boundary conditions associated with the quantum inverse problem for a discrete nonlinear integrable system and its connection to Baxter’s Q-operator
A discrete nonlinear system is analysed in case of open chain boundary conditions at the ends. It is shown that the integrability of the system remains intact, by obtaining a modified set of Lax equations which automatically take care of the boundary conditions. The same Lax pair also conforms to the conditions stipulated by Sklyanin [5]. The quantum inverse problem is set up and the diagonalis...
متن کاملA Lax Operator Hierarchy for the New Fifth Order Integrable System
We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.
متن کامل