Integrability of a discrete Yajima-Oikawa system
arXiv:1804.10224
Abstract
A space discretization of an integrable long wave-short wave interaction model, called the Yajima-Oikawa system, was proposed in the recent paper arXiv:1509.06996 using the Hirota bilinear method (see also https://link.aps.org/doi/10.1103/PhysRevE.91.062902). In this paper, we propose a Lax-pair representation for the discrete Yajima-Oikawa system as well as its multicomponent generalization also considered in arXiv:1509.06996 and prove that it has an infinite number of conservation laws. We also derive the next higher flow of the discrete Yajima-Oikawa hierarchy, which generalizes a modified version of the Volterra lattice. Relations to two integrable discrete nonlinear Schrödinger hierarchies, the Ablowitz-Ladik hierarchy and the Konopelchenko-Chudnovsky hierarchy, are clarified.
17 pages; (v2) minor corrections (v3) added one reference (v4) added two references (v5) added one reference