Liouville integrable defects: the non-linear Schrödinger paradigm

2011/10/31 by Jean Avan, Anastasia Doikou · 1 citation
Mathematics · Physics and Astronomy · #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Hierarchy #Integrable system #Lax pair #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Poisson distribution #Pure mathematics #Quantum mechanics #Schrödinger's cat #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/jhep01(2012)040

published as JHEP 01 (2012) 040 · 22 pages, Latex. Minor misprints corrected

openalex publication_date 2012/01/01 · arxiv created 2012/02/14 · arxiv updated 2012/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

A systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrödinger 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.

Citations

• Jump-defects in the nonlinear Schrödinger model and other non-relativistic field theories
• Systematic classical continuum limits of integrable spin chains and emerging novel dualities
• The generalized non-linear Schrödinger model on the interval
• An Algebraic Setting for Defects in the XXZ and Sine-Gordon Models

Cited by

• The sine-Gordon model in the presence of defects