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 6×6 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.
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BibTeX
@misc{lu2026higherorder,
title = {{Higher-order semi-rational solutions of the (2+1)-dimensional nonlocal multi-component Yajima--Oikawa system}},
author = {Wenqiang Lu and Kelei Tian and Ying Xu and Ge Yi and Xiaoming Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14949},
eprint = {2610.14949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14949},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Higher-order semi-rational solutions of the (2+1)-dimensional nonlocal multi-component Yajima--Oikawa system
AU - Wenqiang Lu
AU - Kelei Tian
AU - Ying Xu
AU - Ge Yi
AU - Xiaoming Zhu
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14949
UR - https://arxiv.org/abs/2610.14949
AB - 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 6×6 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.
ER -