After the (1 + 1)-dimensional nonlinear Schrodinger equation is embedded in higher dimensions and the usual singularity analysis approach is extended such that all the Painleve expansion coefficients are conformal invariant, many higher dimensional integrable models are got after the nontrivial conformal invariant expansion coefficients are taken to be zero simply. The Painleve properties of the obtained higher dimensional models (including some (3 + 1)-dimensional models) are proved.
