Journal of Mathematics Research; Vol. 4, No. 6; 2012 ISSN 1916-9795 E-ISSN 1916-9809 Published by Canadian Center of Science and Education A Note on Exact Solutions of Coupled (2+1)-dimensional Nonlinear Systems of Schrodinger¨ Equations Yingqing Song1 & Zaiyun Zhang2 1 School of Mathematics and Computation Sciences, Hunan City University, Yiyang, Hunan Province, China 2 School of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan Province, China Correspondence: Zaiyun Zhang, School of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, Hunan Province, China. E-mail:
[email protected] Received: July 1, 2012 Accepted: July 26, 2012 Online Published: November 26, 2012 doi:10.5539/jmr.v4n6p121 URL: http://dx.doi.org/10.5539/jmr.v4n6p121 Abstract In this paper, we investigate the coupled (2+1)-dimensional nonlinear systems of Schrodinger¨ equations given in Khani, Darvishi, Farmany and Kavitha (2010) and obtain exact traveling solutions by using the modified trigono- G metric function series method, the modified ( G )-expansion method and First Integral Method respectively. Keywords: Schrodinger¨ equation, exact solution, modified trigonometric function series method(MTFSM), mod- G ified ( G )-expansion method, First Integral Method (FIM) PACS numbers: 04.20.Jb, 52.35.Sb, 02.30.Jr 1. Introduction It is well known that traveling wave solutions of Nonlinear Partial Differential Equations (NPDEs) play an impor- tant role in the study of nonlinear wave phenomena. The wave phenomena are observed in fluid