×

Application of exp-function method to high-dimensional nonlinear evolution equation. (English) Zbl 1142.35593

Summary: In this paper, the exp-function method is used to obtain generalized solitonary solutions and periodic solutions of the (\(3 + 1\))-dimensional Kadomtsev-Petviashvili equation. It is shown that the exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolution equations in mathematical physics.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35Q51 Soliton equations

Software:

Mathematica
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ablowitz, M.J.; Clarkson, P.A., Soliton, nonlinear evolution equations and inverse scattering, (1991), Cambridge University Press New York · Zbl 0762.35001
[2] Hirota, R., Phys rev lett, 27, 1192, (1971)
[3] Miurs, M.R., Bachklund 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] Wang, M.L., Phys lett A, 213, 279, (1996)
[7] El-Shahed, M., Int J nonlinear sci numer simul, 6, 163, (2005)
[8] He, J.H., Int J nonlinear sci numer simul, 6, 207, (2005)
[9] He, J.H., Chaos, solitons & fractals, 26, 695, (2005)
[10] He, J.H., Int J nonlinear mech, 34, 699, (1999)
[11] He, J.H., Appl math comput, 114, 115, (2000)
[12] He, J.H., Chaos, solitons & fractals, 19, 847, (2004)
[13] He, J.H., Phys lett A, 335, 182, (2005)
[14] He, J.H., Int J modern phys B, 20, 1141, (2006)
[15] He JH. Non-perturbative methods for strongly nonlinear problems, Dissertation. de-Verlag im Internet GmbH, Berlin, 2006.
[16] Abassy, T.A.; El-Tawil, M.A.; Saleh, H.K., Int J nonlinear sci numer simul, 5, 327, (2004)
[17] Malfliet, W., Am J phys, 60, 650, (1992)
[18] Zayed, E.M.E.; Zedan, H.A.; Gepreel, K.A., Int J nonlinear sci numer simul, 5, 221, (2004) · Zbl 1069.35080
[19] Abdusalam, H.A., Int J nonlinear sci numer simul, 6, 99, (2005)
[20] Zhang, S.; Xia, T.C., Commun theor phys (Beijing, China), 45, 985, (2006)
[21] Zhang, S., Chaos, solitons & fractals, 31, 951, (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] Liu, S.K.; Fu, Z.T.; Liu, S.D.; Zhao, Q., Phys lett A, 289, 69, (2001)
[26] Dai, C.Q.; Zhang, J.F., Solitons & fractals, 27, 1042, (2006)
[27] Zhao, X.Q.; Zhi, H.Y.; Zhang, H.Q., Chaos, solitons & fractals, 28, 112, (2006)
[28] Zhou, Y.B.; Wang, M.L.; Wang, Y.M., Phys lett A, 308, 31, (2003)
[29] Li, X.Y.; Yang, S.; Wang, M.L., Chaos, solitons & fractals, 25, 629, (2005)
[30] Zhang, S., Phys lett A, 358, 414, (2006)
[31] Zhang, S., Chaos, solitons & fractals, 30, 1213, (2006)
[32] He, J.H.; Wu, X.H., Chaos, solitons & fractals, 30, 700, (2006)
[33] Wang, L.Y.; Lou, S.Y., Commun theor phys (Beijing, China), 33, 683, (2000)
[34] Senthivelan, M., Appl math comput, 123, 386, (2001)
[35] Bai, C.L.; Bai, C.J.; Zhao, H., Commun theor phys (Beijing, China), 44, 821, (2005)
[36] Zhao, Q.; Liu, S.K.; Fu, Z.T., Commun theor phys (Beijing, China), 42, 239, (2004)
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.