Some Wadati-Konno-Ichikawa type integrable systems and their constructions

Abstract

A standard-form Wadati-Konno-Ichikawa(WKI) type integrable hierarchy is derived from a corresponding matrix spectral problem associated with the Lie algebra sl(2, R). 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 generalized short pulse equation arises naturally from the negative WKI flow.