The Painlev'e analysis and reducibility to the canonical forms for nonautonomous soliton equations in higher-dimensions and their exact solutions

Abstract:
It is showed mainly that new nonautonomous KdV and NLS equations in $(2+ 1)$ dimensions have the complete integrability under suitable conditions of variable coefficients. The conditions are determined via the Painlev'e analysis that Weiss and his collaborators have introduced. Furthermore, setting the above conditions, the nonautonomous soliton equations may be reduced into the well-known canonical forms by changes of independent variables.

And exacts solutions and its hierarchy are obtained for special cases of equations constructed.