  We determine all cases when there exists a meromorphic solution of the third
order ODE describing traveling waves solutions of the Kuramoto-Sivashinsky
equation. It turns out that there are no other meromorphic solutions besides
those explicit solutions found by Kuramoto and Kudryashov. The general method
used in this paper, based on Nevanlinna theory, is applicable to finding all
meromorphic solutions of a wide class of non-linear ODE.
  Keywords: Kuramoto and Sivashinsky equation, meromorphic functions, elliptic
functions, Nevanlinna theory.
