AI 中文总结
研究非线性薛定谔方程第 N 阶有理 rogue 波，通过三项递推关系生成该序列，相比之前方法更简便，能得到含六个任意复参数的第七阶波，为研究新模式存在性提供可能。
AI 中文摘要
非线性薛定谔方程（NLS）的第 N 阶有理 rogue 波依赖于 2N - 2 个实参数，已证明无法通过非线性叠加公式生成。本文通过三项递推关系生成该序列，每一步仅需计算 2N - 2 个变量的三个 N - 1 阶行列式，而之前方法需 2N 个变量的两个 2N 阶行列式。借此明确得到具有六个任意复参数的第七阶波，其简洁表达式为研究除已观察到的（同心环、多边形构型等）之外新模式的可能存在提供了可能。
英文摘要
The $N$-th order rational rogue wave of the nonlinear Schrödinger equation (NLS), which depends on $2 N-2$ real parameters, has been shown to be impossible to generate by the nonlinear superposition formula. We here generate this sequence by a three-term recurrence relation, each step only requiring the computation of three $N-1$-th order determinants of $2 N-2$ variables, while the previous method requires two determinants of order $2 N$ in $2 N$ variables. This allows us to obtain explicitly the seventh wave with its six arbitrary complex parameters. These very compact expressions open the possibility to investigate the possible existence of new patterns in addition to the already observed ones (concentric rings, polygonal configurations, \dots).
Comments13 pages, 5 supplementary files, to appear, Journal of mathematical physics
