A novel discretization of the Yajima-Oikawa equation: Cauchy matrix approach

The Cauchy matrix approach, rooted in the Sylvester equation, plays a crucial role in defining the τ functions of nonlinear evolution equations. In this paper, the Cauchy matrix approach is employed to introduce a novel integrable semi-discrete counterpart of the one-dimensional Yajima-Oikawa (YO) system. This new system is linked with the differential-difference Kadomtsev-Petviashvili (KP) equation with self-consistent sources (SCS). Based on the Cauchy matrix approach of the KP system, we systematically construct multiple soliton and multiple pole solutions. Furthermore, we analyze and illustrate various examples of soliton solutions for further understanding.