zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
35Q53KdV-like (Korteweg-de Vries) equations
35-04Machine computation, programs (partial differential equations)
35Q51Soliton-like equations
Software:
Mathematica
WorldCat.org
Full Text: DOI
References:
[1] Ablowitz, M. J.; Clarkson, P. A.: Soliton, nonlinear evolution equations and inverse scattering, (1991) · Zbl 0762.35001
[2] Hirota, R.: Phys rev lett, Phys rev lett 27, 1192 (1971)
[3] Miurs, M. R.: Bachklund transformation, (1978)
[4] Weiss, J.; Tabor, M.; Carnevale, G.: J math phys, J math phys 24, 522 (1983)
[5] Yan, C.: Phys lett A, Phys lett A 224, 77 (1996)
[6] Wang, M. L.: Phys lett A, Phys lett A 213, 279 (1996)
[7] El-Shahed, M.: Int J nonlinear sci numer simul, Int J nonlinear sci numer simul 6, 163 (2005)
[8] He, J. H.: Int J nonlinear sci numer simul, Int J nonlinear sci numer simul 6, 207 (2005)
[9] He, J. H.: Chaos, solitons & fractals, Chaos, solitons & fractals 26, 695 (2005)
[10] He, J. H.: Int J nonlinear mech, Int J nonlinear mech 34, 699 (1999)
[11] He, J. H.: Appl math comput, Appl math comput 114, 115 (2000)
[12] He, J. H.: Chaos, solitons & fractals, Chaos, solitons & fractals 19, 847 (2004)
[13] He, J. H.: Phys lett A, Phys lett A 335, 182 (2005)
[14] He, J. H.: Int J modern phys B, 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, Int J nonlinear sci numer simul 5, 327 (2004)
[17] Malfliet, W.: Am J phys, Am J phys 60, 650 (1992)
[18] Zayed, E. M. E.; Zedan, H. A.; Gepreel, K. A.: Int J nonlinear sci numer simul, Int J nonlinear sci numer simul 5, 221 (2004)
[19] Abdusalam, H. A.: Int J nonlinear sci numer simul, Int J nonlinear sci numer simul 6, 99 (2005)
[20] Zhang, S.; Xia, T. C.: Commun theor phys (Beijing, China), Commun theor phys (Beijing, China) 45, 985 (2006)
[21] Zhang, S.: Chaos, solitons & fractals, Chaos, solitons & fractals 31, 951 (2007)
[22] Hu, J. Q.: Chaos, solitons & fractals, Chaos, solitons & fractals 23, 391 (2005)
[23] Yomba, E.: Chaos, solitons & fractals, Chaos, solitons & fractals 27, 187 (2006)
[24] Zhang, S.; Xia, T. C.: Phys lett A, Phys lett A 356, 119 (2006)
[25] Liu, S. K.; Fu, Z. T.; Liu, S. D.; Zhao, Q.: Phys lett A, Phys lett A 289, 69 (2001)
[26] Dai, C. Q.; Zhang, J. F.: Solitons & fractals, Solitons & fractals 27, 1042 (2006)
[27] Zhao, X. Q.; Zhi, H. Y.; Zhang, H. Q.: Chaos, solitons & fractals, Chaos, solitons & fractals 28, 112 (2006)
[28] Zhou, Y. B.; Wang, M. L.; Wang, Y. M.: Phys lett A, Phys lett A 308, 31 (2003)
[29] Li, X. Y.; Yang, S.; Wang, M. L.: Chaos, solitons & fractals, Chaos, solitons & fractals 25, 629 (2005)
[30] Zhang, S.: Phys lett A, Phys lett A 358, 414 (2006)
[31] Zhang, S.: Chaos, solitons & fractals, Chaos, solitons & fractals 30, 1213 (2006)
[32] He, J. H.; Wu, X. H.: Chaos, solitons & fractals, Chaos, solitons & fractals 30, 700 (2006)
[33] Wang, L. Y.; Lou, S. Y.: Commun theor phys (Beijing, China), Commun theor phys (Beijing, China) 33, 683 (2000)
[34] Senthivelan, M.: Appl math comput, Appl math comput 123, 386 (2001)
[35] Bai, C. L.; Bai, C. J.; Zhao, H.: Commun theor phys (Beijing, China), Commun theor phys (Beijing, China) 44, 821 (2005)
[36] Zhao, Q.; Liu, S. K.; Fu, Z. T.: Commun theor phys (Beijing, China), Commun theor phys (Beijing, China) 42, 239 (2004)