HAMILTONIAN-STRUCTURE OF THE SUPER EVOLUTION EQUATION

The constrained variational calculus proposed in previous papers [Y. Zheng, Y. Li, and D. Chen, Sci. Sinica A 24, 138 (1986); G. Tu, Kexue Tangbao 29, 1227 (1984)] is generalized to the supersymmetric case. Utilizing this method to some super AKNS system, which has soliton solutions and conserved quantities, their equations of motion with the Hamiltonian structure can be written as a 4×4 matrix. This is the supersymmetric symplectic matrix and hn are Hamiltonians of the system. The conserved quantities worked out in recent literature are just the first few terms of our analytic expression.