Painlev analysis and integrability of systems of nonlinear partial differential equations

Abstract

The method of Painleve analysis is introduced and used to explore the integrability of certain physically significant nonlinear partial differential equations (nPDEs). These nPDEs include the Burgers’ equation, Korteweg-de Vries equation (KdV) and nonlinear Klein-Gordon equation. Furthermore, it is shown primarily that this Painleve test is intended to determine necessary conditions for such class of nPDEs to have the Painleve property. However, the nonlinear Klein-Gordon equation is shown instead to be integrable with respect to the Weak Painlevé test.