Analytic solitary waves of nonintegrable equations

A major drawback of most methods to find analytic expressions for solitary waves is the a priori restriction to a given class of expressions. To overcome this difficulty, we present a new method, applicable to a wide class of autonomous equations, which builds as an intermediate information the first order autonomous ordinary differential equation (ODE) satisfied by the solitary wave. We discuss its application to the cubic complex one-dimensional Ginzburg–Landau equation, and conclude to the elliptic nature of the yet unknown most general solitary wave.