The generalized non-linear Schrödinger model on the interval

2007/06/30 by Anastasia Doikou, Davide Fioravanti, Francesco Ravanini
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2007.08.007

published as Nucl.Phys.B790:465-492,2008 · 33 pages, Latex. Minor misprints corrected

openalex publication_date 2007/08/28 · arxiv created 2008/01/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The generalized (1+1)-D non-linear Schrodinger (NLS) theory with particular integrable boundary conditions is considered. More precisely, two distinct types of boundary conditions, known as soliton preserving (SP) and soliton non-preserving (SNP), are implemented into the classical gl_N NLS model. Based on this choice of boundaries the relevant conserved quantities are computed and the corresponding equations of motion are derived. A suitable quantum lattice version of the boundary generalized NLS model is also investigated. The first non-trivial local integral of motion is explicitly computed, and the spectrum and Bethe Ansatz equations are derived for the soliton non-preserving boundary conditions.

Citations

• A Novel Long Range Spin Chain and PlanarN=4 Super Yang-Mills
• The Highest Weight Property for the SU_q(n) Invariant Spin Chains
• Boundary conditions for integrable quantum systems