A new Lie algebra and corresponding evolution equations hierarchy

In this paper, an extension of Lie algebra An-1An-1 was proposed [Zhang YF. Phys Lett A 2003;310:19, Xia TC, Chen XH, Chen DY. Chaos, Solitons & Fractals 2005;23:1033]. Based on that extension, we presented a new Lie algebra. Meanwhile we obtained the corresponding hierarchy of evolution equations and it was shown that the corresponding hierarchy of evolution equations was integrable in Liouville sense. Integrable couplings of the new hierarchy was obtained by using loop algebra G∼ . Finally, the Hamiltonian form of a binary symmetric constrained flows of the system was given.