2007/04/30 by V. Caudrelier · 1 citation
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #nlin.SI
paper · pdf · doi:10.1142/s0219887808003223
published as IJGMMP vol.5, No. 7 (2008), 1085-1108 · 27 pages, no figures. Final version accepted for publication. References added and section 5 amended
arxiv created 2009/01/14 · arxiv updated 2015/05/12
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.