Polynomial conservation laws of the generalized Emden-Fowler equation

Abstract

In this paper we consider the polynomial conservation laws of fourth degree with respect to ẋ of the generalized Emden-Fowler's equation ẍ + bt-1ẋ + λxxtk = 0. It is demonstrated that the existence of conservation laws depends upon the solution of a system of partial differential equations, usually termed the generalized Killing's equations. The general form of the fourth degree conservation laws of the Emden-Fowler equation is given and some concrete examples are discussed. © 1997 Elsevier Science Ltd.