Liouville integrable defects: the non-linear Schrodinger paradigm

Abstract

A systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrodinger model in the presence of a single particle-like defect is investigated through this algebraic approach. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. Coincidence of our results with the continuum limit of the discrete expressions obtained in earlier works further confirms our approach.

22 pages, Latex. Minor misprints corrected

References in corpus (9)

• Quantum and classical integrable sine-Gordon model with defect
• On purely transmitting defects in affine Toda field theory
• Type-II Bäcklund Transformations via Gauge Transformations
• A transmission matrix for a fused pair of integrable defects in the sine-Gordon model
• The generalized non-linear Schrodinger model on the interval
• Comments on defects in the a_r Toda field theories
• Defects in the discrete non-linear Schrodinger model
• 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 (28)

• Interplay between the Inverse Scattering Method and Fokas's Unified Transform with an Application
• Type-II Bäcklund Transformations via Gauge Transformations
• Lagrangian and Hamiltonian structures in an integrable hierarchy and space-time duality
• On the Inverse Scattering Method for Integrable PDEs on a Star Graph
• A multisymplectic approach to defects in integrable classical field theory
• 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
• Multisymplectic approach to integrable defects in the sine-Gordon model
• Darboux-Backlund transformations, dressing & impurities in multi-component NLS
• Classical impurities associated to high rank algebras
• Type-II defects in the super-Liouville theory
• Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model
• Multiform description of the AKNS hierarchy and classical r-matrix
• N=1 super sinh-Gordon model with defects revisited
• Defects in the supersymmetric mKdV hierarchy via Backlund transformations
• On classical and semiclassical properties of the Liouville theory with defects
• Integrability of generalised type II defects in affine Toda field theory
• Jumps and twists in affine Toda field theories
• Type-I integrable quantum impurities in the Heisenberg model
• Infinite dimension reflection matrices in the sine-Gordon model with a boundary
• Transmission amplitudes from Bethe ansatz equations
• Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains
• The sine-Gordon model in the presence of defects
• Lax pair formulation in the simultaneous presence of boundaries and defects
• The classical nonlinear Schrödinger model with a new integrable boundary
• Time-dependent defects in integrable soliton equations
• On the nonlinear Schrödinger equation with a time-dependent boundary condition