Abstract
•Generalization of the classical WKI hierarchy by adding a suitable nonlinear term is derived for the first time.•This new hierarchy possesses a bi-Hamiltonian structure which is furnished by the trace identity.•The symbolic computation Maple is used to deal with some complex process.
With the aid of symbolic computation by Maple, a new integrable generalization of the classical Wadati–Konno–Ichikawa 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, and possesses infinitely many independent commuting symmetries and conservation laws.