Geometric Bäcklund-Darboux transformations for the KP hierarchy


Helminck, Gerard F. and Leur, Johan W. van de (2001) Geometric Bäcklund-Darboux transformations for the KP hierarchy. Publications of the Research Institute for Mathematical Sciences, 37 (4). pp. 479-519. ISSN 0034-5318

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Abstract:In this paper it is shown that, if you have two planes in the Sato Grassmannian that have an intersection of finite codimension, then the corresponding solutions of the KP hierarchy are linked by Bäcklund-Darboux (shortly BD-)transformations. The pseudodifferential operator that performs this transformation is shown to be built up in a geometric way from so-called elementary BD-transformations and is given here in a closed form. The corresponding action on the tau-function, associated to a plane in the Grassmannian, is also determined.
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Additional information:Open Access
Copyright:© 2001 Research Institute for Mathematical Sciences
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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