Liouville integrable defects: the non-linear Schrodinger paradigm

Details Liouville integrable defects: the non-linear Schrodinger paradigm Liouville integrable defects: the non-linear Schrodinger paradigm

2011-10-21

arxiv.org/abs/1110.4728v4

JHEP 01 (2012) 040

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, Latex. Minor misprints corrected

Scientific paper

10.1007/JHEP01(2012)040

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.

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