{"title":"New Exact Three-Wave Solutions for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov System","authors":"Fadi Awawdeh, O. Alsayyed","volume":64,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":474,"pagesEnd":477,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/296","abstract":"
New exact three-wave solutions including periodic two-solitary solutions and doubly periodic solitary solutions for the (2+1)-dimensional asymmetric Nizhnik-Novikov- Veselov (ANNV) system are obtained using Hirota's bilinear form and generalized three-wave type of ansatz approach. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an e¤ective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.<\/p>\r\n","references":"[1] M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering. Lecture Notes Series, vol. 149. Cambridge University Press, Cambridge (1991). \r\n[2] F. Awawdeh, New exact solitary wave solutions of the Zakharov-Kuznetsov equation in the electron-positron-ion plasmas, Appl. Math. Comput. 218 (2012) 7139-7143.\r\n[3] F. Awawdeh, H. M. Jaradat, S. Al-Shara', Application of a simplified bilinear method to ion- acoustic solitary waves in plasma, Eur. Phys. J. D., doi:10.1140\/epjd\/e2011-20518-0, 2012. \r\n[4] M Boiti, j. Leon, M. Manna and F pempinelli, On the spectral transform of a Korteweg-de Vries equation in two spatiral dimentions, Inverse Probl. 2 (1986) 271.\r\n[5] Z. Dai, S. Lin Ha. Fu and X. Zeng, Exact three-wave solutions for the KP equation, Appl. Math. Comput. 216 (2010) 1599-1604.\r\n[6] C. Dai, S. Wu and X. Cen, New Exact Solutions of the (2+1)- Dimensional Asymetric Nizhnik-Novikov- Veselov System, Int J Theor Phys 47 (2008) 1286-1293.\r\n[7] C. Dai and Y. Wang, New variable separation solutions of the (2+1)-dimentional asymmetric Nizhnik-Novikov-Veselov system, Nonlinear Analysis 71 (2009) 1496-1503. \r\n[8] P. G. Estevez, S. Leble, A wave equation in (2+1): Painleve analysis and solutions, Inverse Problems 11 (1995) 945. \r\n[9] C. S. Gardner, J. M. Green, M. D. Kruskal, R.M. Miura, Method for solving the Korteweg-de Vries equation, Phys. Rev. Lett. 19 (1967) 1095-1097.\r\n[10] R. Hirota, Direct methods in solution theory, in: R. K. Bullough, P. J. Caudrey (Eds.), Solitons, Springer, Berlin, 1980. \r\n[11] R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solutions, Phys. Rev. Lett. 27 (1971) 1192-1194.\r\n[12] R. Hirota, Y. Ohta, Hierarchies of coupled soliton equations. I, j. Phys. Soc. Japan 60 (1991) 798-809. \r\n[13] R. Hirota, J. Satsuma, A variety of nonlinear network equations generated from the Bcklund transformation for the Tota lattice, Suppl. Progr. Theoret. Phys. 59 (1976) 64-100.\r\n[14]H. C. Hu, X. Y. Tang, S. Y. Lou and q. p. Liu, Chaos Solitons Fractals 22 (2004) 327.\r\n[15] H.M Jaradat, S. Al- Shara' , F. Awawdeh, M. Alquran, Variable coefficient equations of the Kadomtsev- Petviashvili hierarchy: multiple soliton solutions and singular multiple soliton solutions, Phys Scr. 85 (2012) 035001.\r\n[16]E. J. Parkes, B. R. Duffy, An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Commun. Comput. Phys. 98 (1996) 288-300.\r\n[17] A. Wazwaz, Multiple soliton solutions for the (2+1)-dimentional asymmetric Nizhnik-Novikov-Veselov equation, Nonlinear Analysis 72 (2010) 1314-1318.\r\n[18] G. Yu and H. Tam, A vector asymemetrical NNV eqution: Soliton solutions, bilinear Backlund transformation and Lax pair, J. Math. Anal. Appl. 344 (2008) 593-600.\r\n[19] F. Zhaosheng, Comment on \"On the extended applications of homogeneous balance method\", Appl. Math. Comput. 158 (2) (2004) 593-596.\r\n[20] j. Zhang, Homogeneous balance method and chaotic and fractal solutions for the Nizhnik-Novikov-Veselov equation, Physics Letters A 313 (2003) 401-407. ","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 64, 2012"}