Departmental Bulletin Paper Discretisations of Constrained KP Hierarchies

Willox, Ralph  ,  Hattori, Madoka

22 ( 3 ) 2015-07-15 , Graduate School of Mathematical Sciences, The University of Tokyo , Graduate School of Mathematical Sciences, The University of Tokyo , Nippon Life Insurance Company, Actuarial Department
We present a discrete analogue of the so-called symmetry reduced or ‘constrained’ KP hierarchy. As a result we obtain integrable discretisations, in both space and time, of some well-known continuous integrable systems such as the nonlinear Schr¨odinger equation, the Broer-Kaup equation and the Yajima-Oikawa system, together with their Lax pairs. It will be shown that these discretisations also give rise to a discrete description of the entire hierarchy of associated integrable systems. The discretisations of the Broer-Kaup equation and of the Yajima-Oikawa system are thought to be new.

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