Liouville integrable defects: the non-linear Schrodinger paradigm
High Energy Physics - Theory
2012-02-15 v4 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1110.4728,
title = {Liouville integrable defects: the non-linear Schrodinger paradigm},
author = {Jean Avan and Anastasia Doikou},
journal= {arXiv preprint arXiv:1110.4728},
year = {2012}
}
Comments
22 pages, Latex. Minor misprints corrected