A new loop algebra and the corresponding computing formula of constant gamma in the quadratic-form identity, as well as the generalized Burgers hierarchy

摘要

A new loop algebra containing four arbitrary constants is presented, and the corresponding computing formula of constant gamma in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant gamma in the trace identity. As application, a new Liouville integrable hierarchy which possess bi-Hamiltonian structure and generalized Burgers hierarchy are derived.