The Conjugate Equation Approach for Finding the Hamiltonian Structure of Soliton Equation

We estabilished a corresponding relation between the zero curvature equation and its conjugate representation for a general spectral problem. Using this relation, we developed a new approach of determining the Hamiltion structures of Nonlinear Evolution Equations (NLEEs), which is simpler and has more application than other approaches. Furthermore, we obtained some results about conservation laws of NLEEs especially for AKNS spectral problem, i.e. quantity Δ is the generator of both conservate density and a conservate fluid.