Non-uniform Coupled Nonlinear Schrödinger Equations Covariant Prolongation Structure Theory

It is well known that the W-E's prolongation structure is a powerful method to deal with a lot of nonlinear evolution equations. But its equations are no-covariant.In this paper, for the first time, the covariant prolongation structure theory is applied to coupled inhomogeneous nonlinear Schrodinger equations. By means of the fundamental equations based on the covariant prolongation structure theory, we construct the forms of the integrable equations in two cases. At the same time, we find out the corresponding Lax representations and the corresponding Riccati equations of those equations by using this theory. Furthermore, the Backlund transformations of integrable equations are also discussed. Finally, their one-soliton solutions are obtained respectively.