Studies in Mathematical Sciences Vol. 3, No. 1, 2011, pp. 1-9 DOI: 10.3968/j.sms.1923845220110301.105 ISSN 1923-8444 [Print] ISSN 1923-8452 [Online] www.cscanada.net www.cscanada.org New Soliton Solutions for Systems of Nonlinear Evolution Equations by the Rational Sine-Cosine Method Marwan Alquran 1,* ; Kamel Al-Khaled 2 ; Hasan Ananbeh 3 1 Department of Mathematics and Statistics, Jordan University of Science and Technology, IRBID 22110, Jordan 2 Department of Mathematics and Statistics, Jordan University of Science and Technology, IRBID 22110, Jordan Email: kamel@just.edu.jo 3 Department of Mathematics and Statistics, Jordan University of Science and Technology, IRBID 22110, Jordan Email:hasan ennab@yahoo.com * Corresponding author. Address: Department of Mathematics and Statistics, Jordan University of Science and Technology, IRBID 22110, Jordan. Email: marwan04@just.edu.jo Received 28 July 2011; accepted 18 August 2011 Abstract: In this paper, we construct new solitary solutions to nonlinear PDEs by the rational Sine and Cosine method. Moreover, the periodic solutions and bell-shaped solitons solutions to the Benjamin-Bona- Mahony and the Gardner equations are obtained. New solutions to Broer-Kaup (BK) system are also ob- tained. Finally, the solution of a two-component evolutionary system of a homogeneous KdV equations of order 2 has been investigated by the proposed method. Keywords: Wave variables; Rational Sine-Cosine Method; Nonlinear PDEs; Evolutionary equations Marwan Alquran, Kamel Al-Khaled and Hasan Ananbeh (2011). New Soliton Solutions for Systems of Nonlinear Evo- lution Equations by the Rational Sine-Cosine Method. Studies in Mathematical Sciences, 3(1), 1-9. Available from: URL: http://www.cscanada.net/index.php/sms/article/view/j.sms.1923845220110301.105. DOI: http://dx.doi.org/10.39 68/j.sms.1923845220110301.105. INTRODUCTION It is well known that many models in mathematics and physics are described by nonlinear differential equations. Nowadays, research in physics devotes much attention to nonlinear partial differential evolu- tion model equations, appearing in various fields of science, especially fluid mechanics, solid-state physics, plasma physics, and nonlinear optics [5,9] . Among these nonlinear evolution equations, is the simplest math- ematical known as Benjamin-Bona-Mahony equation, that produce a special kind of soliton solutions [2] , and described by the following normalized system u t = u xxt - u x - uu x . (0.1) The mathematical theory of nonlinear evolution equations starting form KdV equation and the modified KdV (mKdV) equation, contains some important equations, such as Gardner’s equation, that is also known as the mixed KdV-mKdV equation is very widely studied in various area of physics. The Gardner equation shows up, particularly, in the context of internal gravity waves in a density-stratified ocean. The following 1