High-Order Binary Symmetry Constraints of a Liouville Integrable Hierarchy and Its Integrable Couplings

摘要

A 3×3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra _2.Furthermore,high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method.Finally,according to another new subalgebra of loop algebra _2, its integrable couplings are established.