Painlevé Analysis and Exact Solutions of Nonintegrable Systems

Abstract

Here we consider the cubic complex Ginzburg–Landau equation. Applying the Hone’s method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has no elliptic standing wave solutions. This result supplements Hone’s result, that this equation has no elliptic travelling wave solutions. It has been shown that the Hone’s method can be applied to a system of polynomial differential equations more effectively than to an equivalent differential equation.