Study In The Integrability Of Two New Hierarchies Of Nonlinear Evolution Equations

By introducing a two2×2matrix spectral problem, we propose two hierarchies of nonlinear evolution equations. One typical equation in the first hierarchy is the generaliza-tion of sine-Gordon equation. With the aid of trace identity, the Hamiltonian structures and infinite conservation laws of the hierarchy are obtained. A typical equation in the sec-ond hierarchy is the generalized Burgers equation. Based on the nonlinearization method, Liouville integrability is studied.