Abstract
The Gerdjikov-Ivanov(GI) equation can be given from the first non-trivial flow of the generalized Kaup-Newell equations under a reduction condition. In this paper, we perform binary nonlinearization for the generalized Kaup-Newell equations under two symmetry constraints. By imposing the reduction condition on this nonlinearization, we obtain two kinds of new integrable decompositions of the GI equation.
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