Singularity methods for meromorphic solutions of differential equations

Abstract

This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic ordinary differential equations of any order. The examples are taken from physics and include Kuramoto-Sivashinsky and complex Ginzburg-Landau equations.1 Nonlinear systems and their remarkable mathematical structures, ed. N. Euler (CRC Press,