The Hamiltonian Structure of Two Integrable Expanding Models (Journal of Partial Differential Equations, 2020)
In this paper, an extended loop algebra is constructed from which an isospectral problem established. It follows that the integrable couplings of the Tu hierarchy and M-AKNS-KN hierarchy are obtained, and their Hamilton structures are presented by the quadratic-form identity. Moreover, we guarantee that the expanding model we obtained are also Liouville integrable.
Keywords: Integrable coupling; Hamiltonian structure; quadratic-form identity