Discretisations of constrained KP hierarchies

Abstract

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.

arXiv commentAccepted for publication in Journal of Mathematical Sciences, The University of Tokyo

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Cited by in corpus (2)

• Asymptotic diagonalization of the Discrete Lax pair around singularities and conservation laws for dynamical systems
• Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras $A_{N-1}^{(1)}$