×

New solitonary solutions for the MBBM equations using Exp-function method. (English) Zbl 1217.35156

Summary: In this letter we use the Exp-function method for analytic treatment for the modified Benjamin-Bona-Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically change the characteristics of the equations, is examined. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics.

MSC:

35Q51 Soliton equations
68W30 Symbolic computation and algebraic computation
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ablowitz, M.J.; Clarkson, P.A., Soliton, nonlinear evolution equations and inverse scattering, (1991), Cambridge Univ. Press New York · Zbl 0762.35001
[2] Hirota, R., Phys. rev. lett., 27, 1192, (1971)
[3] Miurs, M.R., Backlund transformation, (1978), Springer Berlin
[4] Weiss, J.; Tabor, M.; Carnevale, G., J. math. phys., 24, 522, (1983)
[5] Yan, C., Phys. lett. A, 224, 77, (1996)
[6] Wazwaz, A.M., Math. comput. model., 40, 499, (2004)
[7] E. Yusufoglu, A. Bekir, M. Alp, Chaos Solitons Fractals, doi:10.1016/j.chaos.2006.10.012
[8] Wang, M.L., Phys. lett. A, 213, 279, (1996)
[9] El-Shahed, M., Int. J. nonlinear sci. numer. simul., 6, 163, (2005)
[10] He, J.H., Int. J. nonlinear sci. numer. simul., 6, 207, (2005)
[11] He, J.H., Chaos solitons fractals, 26, 695, (2005)
[12] He, J.H., Int. J. nonlinear mech., 34, 699, (1999)
[13] He, J.H., Chaos solitons fractals, 19, 847, (2004)
[14] Yusufoglu, E., Int. J. nonlinear sci. numer. simul., 8, 2, 153, (2007)
[15] Yusufoglu, E.; Bekir, A., Phys. lett. A, 367, 461, (2007)
[16] E. Yusufoglu, A. Bekir, Chaos Solitons Fractals, doi:10.1016/j.chaos.2006.09.074 · Zbl 1115.35117
[17] Zayed, E.M.E.; Zedan, H.A.; Gepreel, K.A., Int. J. nonlinear sci. numer. simul., 5, 221, (2004) · Zbl 1069.35080
[18] Abdusalam, H.A., Int. J. nonlinear sci. numer. simul., 6, 99, (2005)
[19] Zhang, S.; Xia, T.C., Appl. math. comput., 181, 319, (2006)
[20] El-Wakil, S.A.; Abdou, M.A., Choas solitons fractals, 31, 840, (2007)
[21] El-Wakil, S.A.; Abdou, M.A., Chaos solitons fractals, 31, 1256, (2007)
[22] Hu, J.Q., Chaos solitons fractals, 23, 391, (2005)
[23] Yomba, E., Chaos solitons fractals, 27, 187, (2006)
[24] Zhang, S.; Xia, T.C., Phys. lett. A, 356, 119, (2006)
[25] Zhang, S.; Xia, T.C., Appl. math. comput., 182, 1651, (2006)
[26] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Phys. lett. A, 289, 69, (2001)
[27] Dai, C.Q.; Zhang, J.F., Chaos solitons fractals, 27, 1042, (2006)
[28] Zhao, X.Q.; Zhi, H.Y.; Zhang, H.Q., Chaos solitons fractals, 28, 112, (2006)
[29] Zhang, S., Phys. lett. A, 358, 414, (2006)
[30] Zhang, S., Chaos solitons fractals, 30, 1213, (2006)
[31] Zhang, S., Chaos solitons fractals, 32, 847, (2007)
[32] Abdou, M.A., Chaos solitons fractals, 31, 95, (2007)
[33] He, J.H.; Wu, X.H., Chaos solitons fractals, 30, 700, (2006)
[34] X.H. (Benn)Wu, J.-H. He, Chaos Solitons Fractals, doi:10.1016/j.chaos.2007.01.024
[35] He, J.-H.; Abdou, M.A., Chaos solitons fractals, 34, 1421, (2007)
[36] Zhang, S., Phys. lett. A, 365, 5-6, 448, (2007)
[37] S. Zhang, Chaos Solitons Fractals, doi:10.1016/j.chaos.2006.11.014
[38] Ebaid, A., Phys. lett. A, 365, 3, 213, (2007)
[39] (Benn)Wu, X.-H.; He, J.-H., Comput. math. appl., (2007)
[40] Benjamin, T.B.; Bona, J.L.; Mahony, J.J., Philos. trans. R. soc. London, ser. A, 272, 47, (1972)
[41] Saut, J.C.; Tzetkov, N., Appl. math. res. express, 1, 1, (2004)
[42] Varlamov, V.; Liu, Y., Discrete dynam. syst., 10, 731, (2004)
[43] Wazwaz, A.M.; Helal, M.A., Chaos solitons fractals, 26, 767, (2005)
[44] Wazwaz, A.M., Appl. math. comput., 154, 713, (2004)
[45] Bi, Q., Phys. lett. A, 360, 574, (2007)
[46] E. Yusufoglu, A. Bekir, Chaos Solitons Fractals, doi:10.1016/j.chaos.2007.02.004 · Zbl 1115.35117
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.