Abstract
A standard form of Wadati-Konno-Ichikawa(WKI)-type integrable systems is derived from an sl(2,mathbb {R})-valued spectral problem. Each equation in the resulting hierarchy has a bi-Hamiltonian structure furnished by the trace identity. Then, the higher grading affine algebraic construction of some special cases is proposed. We also show that the generalized short pulse equation arises naturally from the negative WKI flow.
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