The Davey-stewartson Hierarchy And Its Semi-classical Limit

The DS(Davey-Stewartson)hierarchy is one of the most important models in(2+1)dimensional integrable systems.The dispersionless integrable system,which plays an important role in various mathematical and physical nonlinear phenomena,has been a hot topic in recent years.In this paper,we study the DS hierarchy and its dispersionless(semi-classical)limit.Firstly we give a direct algorithm to construct the expression of the DS hierarchy by two scalar pseudo-differential operators.Then we obtain the nonlinear Lax formulation of Hamilton-Jacobi type of the d DS(dispersionless Davey-Stewartson)hierarchy and the flow equations of the d DS hierarchy.After that,we study the semi-classical limit of the DS hierarchy.The two pseudo-differential operators of the DS hierarchy are replaced by two formal Laurent series in the semi-classical limit.The two formal Laurent series are the eigenfunctions of a specific vector field.Finally,we study the connection between the DS hierarchy and the d DS hierarchy.