{"title":"Extend Three-wave Method for the (3+1)-Dimensional Soliton Equation","authors":"Somayeh Arbabi Mohammad-Abadi, Maliheh Najafi","volume":56,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1408,"pagesEnd":1412,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9200","abstract":"
In this paper, we study (3+1)-dimensional Soliton equation. We employ the Hirota-s bilinear method to obtain the bilinear form of (3+1)-dimensional Soliton equation. Then by the idea of extended three-wave method, some exact soliton solutions including breather type solutions are presented.<\/p>\r\n","references":"[1] A.M. Wazwaz,The tanh method: solitons and periodic solutions for the\r\nDodd-Bullough-Tzikhailov and the Tzitzeica-Dodd-Bullough equations,\r\nChaos, Solitons and Fractals 25 (2005)55-63.\r\n[2] Z. Xiqiang, W. Limin, S. Weijun, The repeated homogeneous balance\r\nmethod and its applications to nonlinear partial differential equations,\r\nChaos, Solitons and Fractals, 28(2) (2006) 448-453.\r\n[3] S.J. Liao, Beyond Perturbation: Introduction to the homotopy analysis\r\nmethod, Chapman & Hall\/CRC Press, Boca Raton, 2003.\r\n[4] S.J. Liao, On the homotopy analysis method for nonlinear problems, Appl.\r\nMath. Comput., 147 (2006) 499-513.\r\n[5] S.J. Liao, A general approach to get series solution of nonsimilarity\r\nboundary-layer flows, Commun. Nonlinear Sci. Numer. Simul.,\r\n14(5)(2009) 2144-2159.\r\n[6] M.T. Darvishi, F. Khani, A series solution of the foam drainage equation,\r\nComput. Math. Appl., 58 (2009) 360-368.\r\n[7] A. Aziz, F. Khani, M.T. Darvishi, Homotopy analysis method for variable\r\nthermal conductivity heat flux gage with edge contact resistance,\r\nZeitschrift fuer Naturforschung A, 65a(10)(2010) 771-776.\r\n[8] F. Khani, M.T. Darvishi, R.S.R. Gorla, Analytical investigation for cooling\r\nturbine disks with a non-Newtonian viscoelastic fluid, Comput. Math.\r\nAppl., 61(7)(2011) 1728-1738.\r\n[9] E. Fan, Z. Jian, Applications of the Jacobi elliptic function method to\r\nspecial-type nonlinear equations, Phys. Lett. A, 305(6) (2002) 383-392.\r\n[10] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, Exact three-wave\r\nsolutions for high nonlinear form of Benjamin-Bona-Mahony-Burgers\r\nequations, International Journal of Mathematical and Computer Sciences,\r\n6(3)(2010) 127-131.\r\n[11] M.T. Darvishi, M. Najafi, Some exact solutions of the (2+1)-dimensional\r\nbreaking soliton equation using the three-wave method, International\r\nJournal of Computational and Mathematical Sciences, 6(1)(2012)13-16.\r\n[12] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, New exact solutions\r\nfor the (3+1)-dimensional breaking soliton equation, International Journal\r\nof Information and Mathematical Sciences, 6(2)(2010) 134-137.\r\n[13] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, New application\r\nof EHTA for the generalized (2+1)-dimensional nonlinear evolution\r\nequations, International Journal of Mathematical and Computer Sciences,\r\n6(3)(2010) 132-138.\r\n[14] M.T. Darvishi, M. Najafi, A modification of extended homoclinic test\r\napproach to solve the (3+1)-dimensional potential-YTSF equation, Chin.\r\nPhys. Lett., 28(4)(2011) 040202.\r\n[15] M.T. Darvishi, M. Najafi, Some complexiton type solutions of the (3+1)-\r\ndimensional Jimbo-Miwa equation, International Journal of Computational\r\nand Mathematical Sciences, 6(1)(2012) 25-27.\r\n[16] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, Traveling wave\r\nsolutions for the (3+1)-dimensional breaking soliton equation by (G\u0002\r\nG )-\r\nexpansion method and modified F-expansion method, International Journal\r\nof Computational and Mathematical Sciences, 6(2)(2012) 64-69.\r\n[17] J.H. He, M.A. Abdou,New periodic solutions for nonlinear evolution\r\nequations using Exp-function method, Chaos, Solitons and Fractals, 34\r\n(2007) 1421-1429.\r\n[18] F. Khani, S. Hamedi-Nezhad, M.T. Darvishi, S.-W. Ryu, New solitary\r\nwave and periodic solutions of the foam drainage equation using the Expfunction\r\nmethod, Nonlin. Anal.: Real World Appl., 10 (2009) 1904-1911.\r\n[19] B.-C. Shin, M.T. Darvishi, A. Barati, Some exact and new solutions\r\nof the Nizhnik-Novikov-Vesselov equation using the Exp-function method,\r\nComput. Math. Appl., 58(11\/12) (2009) 2147-2151.\r\n[20] F. Khani, M.T. Darvishi, A. Farmani, L. Kavitha, New exact solutions\r\nof coupled (2+1)-dimensional nonlinear system of Schr\u252c\u00bfodinger equations,\r\nANZIAM Journal, 52 (2010) 110-121.\r\n[21] X.H. Wu, J.H. He, Exp-function method and its application to nonlinear\r\nequations, Chaos, Solitons and Fractals, 38(3)(2008) 903-910.\r\n[22] Z.-D. Dai, S.-Q. Lin, D.-L. Li, G. Mu, The three-wave method for\r\nnonlinear evalution equations, Nonl. Sci. Lett. A 1(1) (2010)77-82.\r\n[23] C.-J. Wang, Z.-D. Dai, L. Liang, Exact three-wave solution for higher\r\ndimensional KDV-type equation, Appl. Math. Comput. 216 (2010.) 501-\r\n505.\r\n[24] J.-O. WU, X.-G. GENG, Grammian Determinant Solution and Pfaffianization\r\nfor a (3+1)-Dimensional Soliton Equation, Commun. Theor.\r\nPhys. (Beijing, China) 52 (2009) 791-794.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 56, 2011"}