New extended direct algebraic method for the Tzitzica type evolution equations arising in nonlinear optics

Document Type : Research Paper


1 Department of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran

2 Faculty of Engineering Technology, Amol University of Special Modern Technologiesl, Amol, Iran

3 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.

4 Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.

5 Department of Mathematics, Cankiri Karatekin University, Cankiri, Turkey.


In this study, the new extended direct algebraic method is exerted for constructing more general exact solutions of the three nonlinear evolution equations with physical interest namely, the Tzitzeica equation, the Dodd-Bullough-Mikhailor equation and the Liouville equation. By using of an appropriate traveling wave transformation reduces these equations to ODE. We state that this method is excellently a generalized form to obtain solitary wave solutions of the nonlinear evolution equations that are widely used in theoretical physics. The method appears to be easier and faster by means of symbolic computation system.