zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Construction of a solitary wave solution for the generalized Zakharov equation by a variational iteration method. (English) Zbl 1141.65386
Summary: The well-known variational iteration method is used to construct solitary wave solutions for the generalized Zakharov equation. The chosen initial solution (trial function) can be in soliton form with some unknown parameters, which can be determined in the solution procedure.

65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
Full Text: DOI
[1] Zakharov, V. E.: Collapse of Langmuir waves. Zh. eksp. Teor. fiz. 62, 1745-1751 (1972)
[2] Golman, M. V.: Langmuir wave solitons and spatial collapse in plasma physics. Physica D 18, 67-76 (1986) · Zbl 0613.76129
[3] Nicolson, D. R.: Introduction to plasma theory. (1983)
[4] Li, L. H.: Langmuir turbulence equations with the self-generated magnetic field. Phys. fluids B 5, 350-356 (1993)
[5] Malomed, B.; Anderson, D.; Lisak, M.: Quiroga-teixeiro ML. Dynamics of solitary waves in the Zakharov model equations. Phys. rev. E 55, 962-968 (1977)
[6] He, J. H.: Application of homotopy perturbation method to nonlinear wave equations. Chaos solitons fractals 26, No. 3, 695-700 (2005) · Zbl 1072.35502
[7] He, J. H.: Limit cycle and bifurcation of nonlinear problems. Chaos solitons fractals 26, No. 3, 827-833 (2005) · Zbl 1093.34520
[8] El-Shahed, M.: Application of he’s homotopy perturbation method to Volterra’s integro-differential equation. Chaos solitons fractals 6, No. 2, 163-168 (2005)
[9] He, J. H.: Approximate solution of nonlinear differential equations with convolution product nonlinearities. Comput. methods appl. Mech. engrg. 167, No. 12, 69-73 (1998) · Zbl 0932.65143
[10] He, J. H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. methods appl. Mech. engrg. 167, No. 12, 57-68 (1998) · Zbl 0942.76077
[11] He, J. H.: Variational iteration method--a kind of non-linear analytical technique: some examples. Int. J. Nonlinear mech. 34, No. 4, 699-708 (1999) · Zbl 05137891
[12] He, J. H.: Variational iteration method for autonomous ordinary differential systems. Appl. math. Comput. 114, No. 2--3, 115-123 (2000) · Zbl 1027.34009
[13] Momani, S.; Abuasad, S.: Application of he’s variational iteration method to Helmholtz equation. Chaos solitons fractals 27, No. 5, 1119-1123 (2006) · Zbl 1086.65113
[14] Soliman, A. A.: A numerical simulation and explicit solutions of KdV-Burgers and Lax’s seventh-order KdV equations. Chaos solitons fractals 29, No. 2, 294-302 (2006) · Zbl 1099.35521
[15] Abulwafa, E. M.; Abdou, M. A.; Mahmoud, A. A.: The solution of nonlinear coagulation problem with mass loss. Chaos solitons fractals 29, No. 2, 313-330 (2006) · Zbl 1101.82018
[16] Odibat, Z. M.; Momani, S.: Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear sci. Numer. simul. 7, No. 1, 27-36 (2006) · Zbl 05675858
[17] He, J. H.: Exp-function method for nonlinear wave equations. Chaos solitons fractals 30, No. 3, 700-708 (2006) · Zbl 1141.35448
[18] J.H. He, M.A. Abdou, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2006.05.072) · Zbl 1152.35441
[19] Wang, M.; Li, X.: Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos solitons fractals 24, No. 5, 1257-1268 (2005) · Zbl 1092.37054
[20] Kaya, D.; El-Sayed, S. M.: A numerical simulation and explicit solutions of the generalized burger--Fisher equation. Appl. math. Comput. 152, 403-413 (2004) · Zbl 1052.65098
[21] Draganescu, G. E.; Capalnasan, V.: Nonlinear relaxation phenomena in polycrystalline solids. Int. J. Nonlinear sci. Numer. simul. 4, No. 3, 219-225 (2003)
[22] Marinca, V.: An approximate solution for one-dimensional weakly nonlinear oscilations. Int. J. Nonlinear sci. Numer. simul. 3, No. 2, 107-120 (2002) · Zbl 1079.34028
[23] M. Javidi, A. Golbabai, Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method, Chaos Solitons Fractals, in press (doi:10.1016/j.chaos.2006.06.088) · Zbl 05235317
[24] He, J. H.; Wu, X. H.: Construction of solitary solution and compacton-like solution by variational iteration method. Chaos solitons fractals 29, No. 1, 108-113 (2006) · Zbl 1147.35338
[25] Bildik, N.; Konuralp, A.: The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations. Int. J. Nonlinear sci. Numer. simul. 7, No. 1, 65-70 (2006) · Zbl 1115.65365
[26] He, J. H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Modern phys. B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039
[27] He, J. H.: Non-perturbative methods for strongly nonlinear problems. (2006)
[28] Soliman, A. A.: Numerical simulation of the generalized regularized long wave equation by he’s variational iteration method. Math. comput. Simul. 70, No. 2, 119-124 (2005) · Zbl 1152.65467
[29] Abdou, M. A.; Soliman, A. A.: Variational iteration method for solving burger’s and coupled burger’s equations. J. comput. Appl. math. 181, No. 2, 245-251 (2005) · Zbl 1072.65127
[30] He, J. H.: Variational theory for linear magneto-electro-elastisity. Int. J. Nonlinear sci. Numer. simul. 2, No. 4, 309-316 (2001) · Zbl 1083.74526
[31] Wang, M.; Li, X.: Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations. Phys. lett. A 343, 48-54 (2005) · Zbl 1181.35255