Poles’ Order of Rational Solutions for Evolution Equations

Abstract

With help of partial fraction expansions theorem ,this paper is an attempt to provide a unifying scheme to the assumptions of rational solutions of partial differential equations, in a natural and simple way. Some new results for linear and nonlinear PDEs have been proved.Moreover, we give an efficient algorithm for obtaining the poles’ order for the solution. Finally, applications of the approach for 1st order linear PDE and the m-KdV equation are presented.