Two types of new integrable decompositions of the Kaup–Newell equation

Two types of new integrable decompositions of the Kaup–Newell equation are presented. The first one comes from the nonstandard binary nonlinearization of the well-known 2 × 2 Kaup–Newell spectral problems and the other comes from the standard binary nonlinearization of new 3 × 3 Kaup–Newell spectral problems. The relationship between them is revealed.