{"title":"Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'\/G)- Expansion Method","authors":"Nisha Goyal, R.K. Gupta","volume":68,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1198,"pagesEnd":1203,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/15030","abstract":"
This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the \u0002G\u0002 G \u0003-expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.<\/p>\r\n","references":"[1] M. Wang, Y. Zhou and Z. Li, Application of a homogeneous balance\r\nmethod to exact solutions of nonlinear equations in mathematical physics,\r\nPhysics Letters A, vol. 216, 1996, pp. 67-75.\r\n[2] X. Zhao, L. Wang and W. Sun, The repeated homogeneous balance\r\nmethod and its applications to nonlinear partial differential equations, Chaos, Solitions and Fractals, vol. 28, 2006, pp. 448-453.\r\n[3] A. M. Wazwaz, New solitary wave and periodic wave solutions to the\r\n(2+1)-dimensional Nizhnik-Nivikov-veselov system, Applied Mathematics\r\nComputation, vol. 187, 2007, pp. 1584-1591.\r\n[4] M. Wang, Solitary wave solutions for variant Boussinesq equations,\r\nPhysics Letters A, vol. 199, 1995, pp. 169-172.\r\n[5] W, Malfielt and W. Hereman, The tanh method: I. Exact solutions of\r\nnonlinear evolution and wave equations, Physica Scripta, vol. 54, 1996,\r\npp. 563-568.\r\n[6] V. A. Arkadiev and A. K. Pogrebkov, Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation, Physica D: Nonlinear Phenomena, vol. 36, 1989, pp. 189-197.\r\n[7] Y. Matsuno, B\u252c\u00bfacklund transformation, conservation laws, and inverse\r\nscattering transform of a model integrodifferential equation for water\r\nwaves, Journal of Mathematical Physics, vol. 31, 1990, pp. 2904-2917.\r\n[8] J. M. Zho and Y. M. Zhang, The Hirota bilinear method for the coupled\r\nBurgers equation and the high-order Boussinesq Burgers equation,\r\nChinese Physics B, vol. 20, 2010, pp. 010205.\r\n[9] M. A. Abdou, Multiple Kink Solutions and Multiple Singular Kink\r\nSolutions for (2+1)-dimensional Integrable Breaking Soliton Equations\r\nby Hirota-s Method, Studies in Nonlinear Science, vol. 2, 2011, pp.\r\n1-4.\r\n[10] M. A. Abdou, An Extended Riccati Equation Rational Expansion Method\r\nand its Applications, International Journal of Nonlinear Science, vol. 7,\r\n2009, pp. 57-66.\r\n[11] X. L. Zhang, J. Wang and N. Q. Zhang, J. Wang and N. Q. Zhang,\r\nA New Generalized Riccati Equation Rational Expansion Method to\r\nGeneralized BurgersFisher Equation with Nonlinear Terms of Any Order,\r\nCommunication in Theoretical Physics, vol. 46, 2006, pp. 779-786.\r\n[12] J. P. Yu and Y. L. Sun, Weierstrass Elliptic Function Solutions to\r\nNonlinear Evolution Equations, Communication in Theoretical Physics,\r\nvol. 50, 2008, pp. 295-298.\r\n[13] Z. Y. Yan, New Doubly Periodic Solutions of Nonlinear Evolution Equations via Weierstrass Elliptic Function Expansion Algorithm, Communication in Theoretical Physics, vol. 42, 2004, pp. 645-648.\r\n[14] A. M. Wazwaz, A sine-cosine method for handlingnonlinear wave\r\nequations, Mathematical and Computer Modelling, vol. 40, 2004, pp.\r\n499-508.\r\n[15] M. Alquran and K. Al-Khaled, The tanh and sinecosine methods for\r\nhigher order equations of Kortewegde Vries type, Physica Scripta, vol.\r\n84, 2011, pp. 025010. [16] S. Zhang and H. Q. Zhang, Discrete Jacobi elliptic function expansion\r\nmethod for nonlinear differential-difference equations, Physica Scripta,\r\nvol. 80, 2009, pp. 045002.[17] W. Zhang, Extended Jacobi Elliptic Function Expansion Method to the\r\nZK-MEW Equation, International Journal of Differential Equations, vol.\r\n2011, 2011, pp. 451420.[18] A. A. Mohammad and M. Can, Painleve Analysis and Symmetries of\r\nthe HirotaSatsuma Equation, Nonlinear Mathematical Physics, vol. 3,\r\n1996, pp. 152-155.\r\n[19] N. Goyal and R. K. Gupta, Symmetries and exact solutions of non\r\ndiagonal Einstein-Rosen metrics, vol. 85, 2012, pp. 015004.\r\n[20] M. Wang, X. Li, J. Zhang, The (G'\/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,\r\nPhysics Letters A, vol. 372, 2008, pp. 417-428.\r\n[21] X. Liu, W. Zhang and Z. Li, Applications of improved (G'\/G)-expansion method to traveling wave solutions of two nonlinear evolution equations, Advances in Applied Mathematics and Mechanics, vol. 4, 2010, pp.\r\n122-130. [22] K. A. Gapreel, A Generalized (G'\/G)-expansion method to find the traveling wave solutions of nonlinear evolution equations, Journal of\r\nPartial Differential Equations, vol. 24, 2011, pp. 55-69. \r\n[23] Y. B. Zhou, C. Li, Application of Modified (G'\/G)-expansion method to traveling wave solutions for Whitham Broer Kaup-Like equations,\r\nCommunication in Theoretical Physics, vol. 51, 2009, pp. 664-670.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 68, 2012"}