Three kinds of nonisospectral integrable model of Wadati–Konno–Ichikawa soliton hierarchies

Abstract

We use the loop algebra to establish two nonisospectral problems. Two nonisospectral WKI hierarchies associated with the nonisospectral problems are derived by means of the symbolic computation by maple. It follows that the corresponding integrable Hamiltonian systems are investigated based on the Tu scheme. Additionally, we deduce the third nonisospectral WKI hierarchy based on the Lenard recursion equations. By reducing the third nonisospectral WKI hierarchy, we obtain the generalized WKI equation.