Two (2Â +Â 1)-dimensional hierarchies of evolution equations and their Hamiltonian structures

Two kinds of appropriate isospectral problems are introduced by using a Lie algebra. With the help of the TAH scheme, we generate two new (2 + 1)-dimensional hierarchies of evolution equations, whose Hamiltonian structures are derived from the trace identity proposed by Tu Guizhang, Andrushkiw R.I. and Huang X.C. Finally, we propose some problems worth thinking about.