1893 Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 6, Issue 11 (June 2011) pp. 1893– 1901 Applications and Applied Mathematics: An International Journal (AAM) Exact Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation by the First Integral Method N. Taghizadeh and M. Mirzazadeh Department of Mathematics Faculty of Mathematics University of Guilan P.O.Box 1914 Rasht, Iran taghizadeh@guilan.ac.ir , mirzazadehs2@guilan.ac.ir Received: August 17, 2010; Accepted: April 29, 2011 Abstract In this paper, the first integral method is used to construct exact travelling wave solutions of Konopelchenko-Dubrovsky equation. The first integral method is algebraic direct method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to non-integrable equations as well as to integrable ones. This method is based on the theory of commutative algebra. Keywords: First integral method; Konopelchenko-Dubrovsky equation. MSC 2010 No.: 35Q53; 35Q80; 35Q55; 35G25. 1. Introduction Nonlinear evolution equations (NLEEs) have been the subject of study in various branches of Mathematical-physical sciences such as physics, biology, and chemistry. The analytical solutions of such equations are of fundamental importance since a lot of mathematical physical models are