Higher-order semi-rational solutions of the (2+1)-dimensional nonlocal multi-component Yajima--Oikawa system

Abstract

Higher-order semi-rational solutions are constructed for the (2+1)-dimensional nonlocal multi-component Yajima-Oikawa system. This system is obtained from its local \(2M\)-component counterpart through a spatial-reflection reduction. Using Hirota's bilinear method and the Kadomtsev-Petviashvili hierarchy reduction, we derive a unified \(6\times6\) block Gram determinant. Its entries involve Schur polynomials and exponential functions. The complex-conjugation and spatial-reflection reductions are imposed through algebraic constraints on the spectral parameters and determinant blocks, with the former ensuring a real-valued denominator tau function. Separate spectral parameter sets are assigned to the rational, breather, and dark-soliton blocks. These solutions describe paired lumps or line rogue waves on breather, dark-soliton, or combined backgrounds. Pure rational, breather, and dark-soliton solutions follow by setting the appropriate block sizes to zero. Asymptotic analysis establishes the elastic interactions of the fundamental breather and dark-soliton pairs and determines their position and phase shifts.