On a systematic approach to defects in classical integrable field theories

Details On a systematic approach to defects in classical integrable field theories On a systematic approach to defects in classical integrable field theories

2007-04-18

arxiv.org/abs/0704.2326v2

IJGMMP vol.5, No. 7 (2008), 1085-1108

Physics

Mathematical Physics

27 pages, no figures. Final version accepted for publication. References added and section 5 amended

Scientific paper

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Backlund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical $r$-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.

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