In this paper, the two-dimension differential transformation method (DTM) is employed to obtain the closed form solutions of the three famous coupled partial differential equation with physical interest namely, the coupled Korteweg-de Vries(KdV) equations, the coupled Burgers equations and coupled nonlinear Schrödinger equation. We begin by showing that how the differential transformation method applies to a linear and non-linear part of any PDEs and apply on these coupled PDEs to illustrate the sufficiency of the method for this kind of nonlinear differential equations. The results obtained are in good agreement with the exact solution. These results show that the technique introduced here is accurate and easy to apply.<\/p>\r\n","references":"[1] A. Borhanifar, Reza Abazari, An unconditionally stable parallel difference\r\nscheme for Telegraph equation, Math. Prob. Eng, vol. 2009, Article ID\r\n969610, 17pages, 2009. http:\/\/doi:10.1155\/2009\/969610.\r\n[2] A. Borhanifar, Reza Abazari, Exact solutions for non-linear Schr\u252c\u00bfodinger\r\nequations by differential transformation method, J. Appl. Math. Comput,\r\nhttp:\/\/doi:10.1007\/s12190-009-0338-2.\r\n[3] A. Borhanifar, Reza Abazari, Numerical study of nonlinear Schr\u252c\u00bfodinger\r\nand coupled Schr\u252c\u00bfodinger equations by differential transformation method,\r\nOpt. Commun, http:\/\/doi:10.1016\/j.optcom.2010.01.046.\r\n[4] Hirota. R, Satsuma. J, Soliton solutions of a coupled Kortewege-de Vries\r\nequation, Phys. Lett. A, 85 (1981), 407-408.\r\n[5] Reza Abazari, A. Borhanifar, Numerical study of Burgers- and coupled\r\nBurgers- equations by differential transformation method, Comput. Math.\r\nAppl, http:\/\/doi:10.1016\/j.camwa.2010.01.039.\r\n[6] Chen. R, Wu. Z, Solving partial differential equation by using multiquadric\r\nquasi-interpolation, Appl.Math.Comput, 186 (2007), 1502-1510.\r\n[7] Xu. Y, Shu. C-W, Local discontinuous Galerkin methods for the\r\nKuramoto- Sivashinsky equations and the Ito-type coupled equations,\r\nComput. Methods. Appl. Mech, 195 (2006), 3430-3447.\r\n[8] Kaya. D, Inan. EI, Exact and numerical traveling wave solutions for\r\nnonlinear coupled equations using symbolic computation, Appl. Math.\r\nComput, 151 (2004), 775-787.\r\n[9] J. Biazar, H. Aminikhah, Exact and numerical solutions for non-linear\r\nBurgers- equation by VIM, Math. Comput. Modelling, 49 (2009) 1394-\r\n1400.\r\n[10] Zayed EME, Zedan HA, Gepreel KA, On the solitary wave solutions\r\nfor nonlinear Hirota Satsuma coupled-KdV of equations, Chaos. Solitons.\r\nFractals, 22 (2004), 285-303.\r\n[11] Caom DB, Yan JR, Zang Y, Exact solutions for a new coupled MKdV\r\nequations and a coupled KdV equations, J. Phys. Lett. A, 297 (2002),\r\n68-74.\r\n[12] Zhang JL, Wang ML, Feng ZD, The improved F-expansion method and\r\nits applications, Phys. Lett. A, 350 (2006), 103-109.\r\n[13] Khater AH, Temsah RS, Hassan MM, A Chebyshev spectral collocation\r\nmethod for solving Burgers type equations, J. Appl. Math. Comput,\r\nhttp:\/\/doi:10.1016\/j.cam.2007.11.007.\r\n[14] Ganji DD, Rafei M, Solitary wave equations for a generalized Hirotasatsuma\r\ncoupled-KdV equation by homotopy perturbation method, Phys.\r\nLett. A, 356 (2006), 131-137.\r\n[15] J.K. Zhou, Differential Transformation and its Application for Electrical\r\nCircuits, Huazhong University Press, Wuhan, China, 1986.\r\n[16] M. Mossa Al-sawalha, M.S.M. Noorani , A numeric-analytic method\r\nfor approximating the chaotic Chen system, Chaos. Soliton. Fract. 42\r\n(2009) 1784-1791.\r\n[17] F. Ayaz, Application of differential transform method to differential-\r\nalgebraic equations, Appl. Math. Comput. 152 (2004) 649-657.\r\n[18] A. Arikoglu, I. Ozkol, Solution of difference equations by using differential\r\ntransform method, Appl. Math. Comput. 174 (2006) 1216-1228.\r\n[19] A. Arikoglu, I. Ozkol, Solution of differential-difference equations by\r\nusing differential transform method, Appl. Math. Comput. 181 (2006)\r\n153-162.\r\n[20] Figen Kangalgil, Fatma Ayaz, Solitary wave solutions for the KdV and\r\nmKdV equations by differential transform method, Chaos. Soliton. Fract.\r\n41 (2009) 464-472.\r\n[21] A. Arikoglu, I. Ozkol, Solution of fractional differential equations by\r\nusing differential transform method, Chaos. Soliton. Fract. 34 (2007)\r\n1473-1481.\r\n[22] Nemat Abazari, Reza Abazari, Solution of nonlinear second-order\r\npantograph equations via differential transform method, International\r\nConference on Computer and Applied Mathematics, October 28-30, 2009,\r\nVenice, Italy (Available at http:\/\/www.waset.org\/journals\/waset\/v58).\r\n[23] A. Arikoglu, I. Ozkol, Solution of boundary value problems for integro-\r\ndifferential equations by using differential transform method, Appl. Math.\r\nComput. 168 (2005) 1145-1158.\r\n[24] Reza Abazari, Solution of Riccati types matrix differential equations\r\nusing matrix differential transform method, J. Appl. Math. & Informatics.\r\n27 (2009), pp. 1133-1143.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 42, 2010"}