The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws

Based on four sets of Lenard recursion sequences and zero-curvature equation, we derive the full positive flows of the Manakov hierarchy associated with a 3×3 matrix spectral problem, from which some new nonlinear evolution equations are proposed. With the help of the Darboux transformation, soliton solutions of two new nonlinear evolution equations in the Manakov hierarchy are constructed. As two special reductions, the full positive flows of the coupled modified Korteweg-de Vries hierarchy and the Sasa-Satsuma hierarchy are deduced, in which some new nonlinear evolution equations are included. And then, we construct the Hamiltonian structures of the Manakov hierarchy and infinite conservation laws of several nonlinear evolution equations.