Painleve analysis and Backlund transformation in the Kuramoto-Sivashinsky equation

The authors apply the Painleve test to the Kuramoto-Sivashinsky nonlinear partial differential equation, which describes many interesting fluid motions. The equation passes the test in a weak sense. Although the Painleve analysis does not yield the general solution, they perform the Backlund transformation in order to obtain new particular solutions. The authors find explicitly all the solutions of the set of equations which define the Painleve-Backlund transformation: they reduce to only one type, namely the already known kink-shaped solitary wave.