Elliptic General Analytic Solutions

In order to flnd analytically the travelling waves of partially integrable au- tonomous nonlinear partial difierential equations, many methods have been pro- posed over the ages: \projective Riccati method", \tanh-method", \exponential method", \Jacobi expansion method", \new ...", etc. The common default to all these \truncation methods" is to only provide some solutions, not all of them. By implementing three classical results of Briot, Bouquet and Poincare, we present an algorithm able to provide in closed form all those travelling waves which are elliptic or degenerate elliptic, i.e. rational in one exponential or rational. Our examples here include the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.

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