Quasi-exact solutions of the dissipative Kuramoto–Sivashinsky equation

• The dissipative Kuramoto–Sivashinsky equation is studied.
• It is shown that this equation does not pass the Painleve test.
• Quasi-exact solutions of the dissipative Kuramoto–Sivashinsky equation is given.

The dissipative Kuramoto–Sivashinsky equation is studied. It is shown that this equation does not pass the Painlevé test and as consequence this equation is not integrable. Quasi-exact solution of the dissipative Kuramoto–Sivashinsky equation is given.