Higher dimensional reciprocal integrable Kaup-Newell systems

The study of integrable systems is one important topics both in physics and mathematics. However, traditional studies on are usually restricted (1+1) (2+1) dimensions. main reasons come from the fact that high-dimensional extremely rare. Recently, we found a large number high dimensional can be derived low ones by means deformation algorithm. In this paper, Kaup-Newell (KN) system extended to (4+1) with help addition original KN system, new also contains three reciprocal forms system. model (<i>D</i>+1) (<inline-formula><tex-math id="M2">\begin{document}$D \leqslant 3$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222418_M2.jpg"/><graphic xlink:href="10-20222418_M2.png"/></alternatives></inline-formula>) systems. Lax integrability symmetry proved. It very difficult solve only investigate traveling wave solutions derivative nonlinear Schrödinger equation. general envelope travelling expressed complicated elliptic integral. single dark (gray) soliton Schödinger equation implicitly written.