Defects in the discrete non-linear Schrodinger model

Abstract

The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.

18 pages, Latex. Comments and clarifications introduced. One reference added

References in corpus (6)

• Quantum and classical integrable sine-Gordon model with defect
• On purely transmitting defects in affine Toda field theory
• The generalized non-linear Schrodinger model on the interval
• Comments on defects in the a_r Toda field theories
• 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 (15)

• Liouville integrable defects: the non-linear Schrodinger paradigm
• The sine-Gordon model with integrable defects revisited
• Sigma models in the presence of dynamical point-like defects
• Classical integrable defects as quasi Bäcklund transformations
• Darboux-Backlund transformations, dressing & impurities in multi-component NLS
• Classical impurities associated to high rank algebras
• Type-I integrable quantum impurities in the Heisenberg model
• Jumps and twists in affine Toda field theories
• Transmission amplitudes from Bethe ansatz equations
• A note on gl_N type-I integrable defects
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• Stochastic analysis & discrete quantum systems
• The sine-Gordon model in the presence of defects
• Lax pair formulation in the simultaneous presence of boundaries and defects
• Selected Topics in Classical Integrability