||Discretisations of Constrained KP Hierarchies
Willox, RalphHattori, Madoka
Journal of mathematical sciences, the University of Tokyo
661 , 2015-07-15 , Graduate School of Mathematical Sciences, The University of Tokyo
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.