Occurrence of secular terms In the Carleman embedding

Abstract

Secular terms occur in many perturbative solutions of nonlinear equation systems. In this work, an investigation is made of which cases they may occur in as the result of the application of the linear Carleman embedding to a system of nonlinear equations. The solution for the embedded system is written in a form that makes it convenient to see how these terms originate. Their occurrence for the general case is discussed and the results are exemplified by working out the Henon-Hei1es system.