A new Lax integrable hierarchy, N Hamiltonian structure and its integrable couplings system

In this Letter, a new isospectral problem is established by choosing subalgebra of loop algebra as its basis. By making use of Tuʹs scheme, the N Hamiltonian structure is established and it is shown that the new hierarchy is integrable in Liouville sense. As two reductions, the two generalized nonlinear Schrödinger equations are obtained, respectively. Integrable couplings of the new hierarchy are obtained by taking a proper algebraic transformation to turn the loop algebra into its equivalent loop algebra like the form of . Finally, the Hamiltonian form of a binary symmetric constrained flows of the system is given.