Discretisations of Constrained KP Hierarchies

J. Math. Sci. Univ. Tokyo
Vol. 22 (2015), No. 3, Page 613–661.

Willox, Ralph ; Hattori, Madoka
Discretisations of Constrained KP Hierarchies
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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 Schrödinger 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.

Keywords: Integrable discretisations, hierarchies, reductions of lattice equations.

Mathematics Subject Classification (2010): Primary 37K10; Secondary 39A10.
Mathematical Reviews Number: MR3408070

Received: 2013-05-29