American Journal of Numerical Analysis, 2013, Vol. 1, No. 1, 32-35 Available online at http://pubs.sciepub.com/ajna/1/1/5 © Science and Education Publishing DOI:10.12691/ajna-1-1-5 Tan-Cot Method to Solve (2+1)-Dimensional Bogoyavlenskii System and Konopelchenko-Dubrovsky Coupled System Anwar Ja'afar Mohamad Jawad * Computer Engineering Technique Department, Al -Rafidain University College, Baghdad, Iraq *Corresponding author: anwar_jawad2001@yahoo.com Received August 02, 2013; Revised November 25, 2013; Accepted December 05, 2013 Abstract In this paper, we establish a traveling wave solution by using the Tan-Cot function algorithm for solving nonlinear partial differential equations. The method is used to obtain new solitary wave solutions for various type of nonlinear partial differential equations such as (2+1)-Dimensional Bogoyavlenskii system, Konopelchenko- Dubrovsky coupled system and the coupled nonlinear evolution equations which are important Soliton equations. Tan-Cot function method has been successfully implemented to establish new solitary wave solutions for the nonlinear PDEs. Keywords: nonlinear PDEs, exact solutions, tan-Cot function method, (2+1)-Dimensional Bogoyavlenskii system, Konopelchenko-Dubrovsky coupled system, the coupled nonlinear evolution equations Cite This Article: Anwar Ja'afar Mohamad Jawad, “Tan-Cot Method to Solve (2+1)-Dimensional Bogoyavlenskii System and Konopelchenko-Dubrovsky Coupled System.” American Journal of Numerical Analysis 1, no. 1 (2013): 32-35. doi: 10.12691/ajna-1-1-5. 1. Introduction Exact solutions to nonlinear partial differential equations NNPDEs play an important role in nonlinear science, especially in nonlinear physical science since they can provide much physical information and more insight into the physical aspects of the problem and thus lead to further applications. Large varieties of physical, chemical, and biological phenomena are governed by nonlinear partial differential equations. One of the most exciting advances of nonlinear science and theoretical physics has been the development of methods to look for exact solutions of nonlinear partialdifferential equations [1]. In recent years, quite a few methods for obtaining explicit traveling and solitary wave solutions of nonlinear evolution equations have been proposed. A variety of powerful methods, such as, tanh-sech method [2,3,4], extended tanh method [5,6,7], hyperbolic function method [8,9], Jacobi elliptic function expansion method [10], F- expansion method [11], and the First Integral method [12,13]. The sine-cosine method [3,14,15] has been used to solve different types of nonlinear systems of PDEs. In this paper, we applied the Tan-Cot method to solve (2+1)-Dimensional Bogoyavlenskii system, Konopelchenko-Dubrovsky coupled system, and the coupled nonlinear evolution equations given respectively by: 2 4 4 4 0 t xxy y x u u uu uv + − − = (1) y x uu v = (2) and 2 2 3 6 3 3 0 2 t xxx x x y x u u buu auu v au v − − + − + = (3) y x u v = (4) and 0 xt xt u vv + = (5) ( ) 3 3 0 t xxx x xx x v v v u v + + + = (6) eqs (1)-(6): indicate that a is scalar. 2. The Tan-Cot Function Method Consider the nonlinear partial differential equation in the form ( ) , , , , , , , , 0 t x y tt xx xy yy Fuu u u u u u u ………… = (7) where u(x, y, t) is a traveling wave solution of nonlinear partial differential equation Eq. (7). We use the transformations, ( ) ( ) , , uxyt f ξ = (8) Where x y t ξ λ = + − (9)