Integrable boundary conditions and modified Lax equations. (English) Zbl 1292.37006
Summary: 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.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
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