The first-integral method applied to the Eckhaus equation

The first-integral method is a direct algebraic method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. In this work, we apply the first-integral method to study the exact solutions of the Eckhaus equation. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.