An integrable semi-discretization of the coupled Yajima--Oikawa system

TL;DR

This paper introduces an integrable semi-discrete version of the coupled Yajima--Oikawa system, providing explicit soliton solutions using Hirota's method and Bäcklund transformations, advancing the understanding of discrete integrable systems.

Contribution

It presents a novel semi-discrete integrable model of the coupled Yajima--Oikawa system with explicit pfaffian soliton solutions, derived from Bäcklund transformations.

Findings

Constructed bright and dark soliton solutions in pfaffian form

Established semi-discrete integrability of the coupled Yajima--Oikawa system

Extended the Bäcklund transformation framework to semi-discrete hierarchy

Abstract

In the present paper, an integrable semi-discrete analogue of the one-dimensional coupled Yajima--Oikawa system, which is comprised of multicomponent short-wave and one component long-wave, is proposed by using Hirota's bilinear method. Based on the reductions of the B\"{a}cklund transformations of the semi-discrete BKP hierarchy, both the bright and dark soliton (for the short-wave components) solutions in terms of pfaffians are constructed.