Classical impurities associated to high rank algebras

Abstract

Classical integrable impurities associated to high rank (gl_N) algebras are investigated. A particular prototype i.e. the vector non-linear Schrödinger (NLS) model is chosen as an example. A systematic construction of local integrals of motion as well as the time components of the corresponding Lax pairs is presented based on the underlying classical algebra. Suitable gluing conditions compatible with integrability are also extracted. The defect contribution is also examined in the case where non-trivial integrable conditions are implemented. It turns out that the integrable boundaries may drastically alter the bulk behavior, and in particular the defect contribution.

18 pages, Latex. Few modifications in the text. Typos corrected

References in corpus (5)

• Quantum and classical integrable sine-Gordon model with defect
• The generalized non-linear Schrodinger model on the interval
• Sigma models in the presence of dynamical point-like defects
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• An Algebraic Setting for Defects in the XXZ and Sine-Gordon Models

Cited by in corpus (7)

• A multisymplectic approach to defects in integrable classical field theory
• Multisymplectic approach to integrable defects in the sine-Gordon model
• Darboux-Backlund transformations, dressing & impurities in multi-component NLS
• Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model
• Jumps and twists in affine Toda field theories
• Lax pair formulation in the simultaneous presence of boundaries and defects
• The classical nonlinear Schrödinger model with a new integrable boundary