2014/06/23 by Willox, Ralph, Hattori, Madoka
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Primary 37K10 #Secondary 39A10
paper · doi:10.48550/arxiv.1406.5828
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 Schroedinger 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.