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)
New soliton solutions of the generalized Zakharov equations using He’s variational approach. (English) Zbl 1211.35071
Summary: We obtain new soliton solutions of the generalized Zakharov equations by He’s well-known variational approach. The condition for continuation of the new solitary solution is obtained.
MSC:
35C08Soliton solutions of PDE
35A15Variational methods (PDE)
References:
[1]He, J. H.: Variational principles for some nonlinear partial differential equations with variable coefficients, Chaos solitons fractals 19, No. 4, 847-851 (2004) · Zbl 1135.35303 · doi:10.1016/S0960-0779(03)00265-0
[2]He, J. H.; Wu, X. H.: Exp-function method for nonlinear wave equations, Chaos solitons fractals 30, No. 3, 700-708 (2006) · Zbl 1141.35448 · doi:10.1016/j.chaos.2006.03.020
[3]He, J. H.: Application of homotopy perturbation method to nonlinear wave equations, Chaos solitons fractals 26, No. 3, 695-700 (2005) · Zbl 1072.35502 · doi:10.1016/j.chaos.2005.03.006
[4]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 · doi:10.1016/j.chaos.2005.10.100
[5]He, J. H.: Some asymptotic methods for strongly nonlinear equations, Internat. J. Modern phys. B 20, No. 10, 1141-1199 (2006) · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[6]Özis, T.; Yıldırım, A.: Application of he’s semi-inverse method to the nonlinear Schrödinger equation, Comput. math. Appl. 54, 1039-1042 (2007) · Zbl 1157.65465 · doi:10.1016/j.camwa.2006.12.047
[7]Tao, Z. L.: Variational approach to the benjamin ono equation, Nonlinear anal. RWA 10, No. 3, 1939-1941 (2009) · Zbl 1168.35304 · doi:10.1016/j.nonrwa.2008.02.031
[8]Ye, Y. H.; Mo, L. F.: He’s variational method for the benjamin–bona–Mahony equation and the Kawahara equation, Comput. math. Appl. (2009)
[9]Zhang, J.: Variational approach to solitary wave solution of the generalized Zakharov equation, Comput. math. Appl. 54, 1043-1046 (2007) · Zbl 1141.65391 · doi:10.1016/j.camwa.2006.12.048
[10]Shang, Yadong; Huang, Yong; Yuan, Wenjun: The extended hyperbolic functions method and new exact solutions to the Zakharov equations, Appl. math. Comput. 200, No. 1, 110-122 (2008) · Zbl 1143.65083 · doi:10.1016/j.amc.2007.10.059
[11]Javidi, M.; Golbabai, A.: Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method, Chaos solitons fractals 36, No. 2, 309-313 (2008)
[12]Omidvar, M.; Barari, A.; Momeni, M.; Ganji, D. D.: New class of solutions for water infiltration problems in unsaturated soils, Int. J. Geomech. geoeng. 5, 127-135 (2010)
[13]Sfahani, M. G.; Ganji, S. S.; Barari, A.; Mirgolbabaei, H.; Domairry, G.: Analytical solutions to nonlinear conservative oscillator with fifth-order non-linearity, Earthq. eng. Eng. vib. 9, No. 3, 367-374 (2010)
[14]He, J. H.: Erratum to: variational principle for two-dimensional incompressible inviscid flow, Phys. lett. A 372, 5858-5859 (2008)
[15]Zakharov, V. E.; Kuznetsov, E. A.: On three-dimensional solitons, Sov. phys. JETP 39, 285-286 (1974)
[16]Korteweg, D. J.; De Vries, G.: On the change of form of long waves advancing in a rectangular channel, and a new type of long stationary waves, Phil. mag. 5, No. 39, 422-443 (1895) · Zbl 26.0881.02
[17]Kadomtsev, B. B.; Petviashvilli, V. I.: On the stability of solitary waves in weakly dispersing media, Sov. phys. Dokl. 15, 539-541 (1970) · Zbl 0217.25004
[18]Grimshaw, R. H. J.; Zhu, Y.: Oblique interaction between internal solitary waves, Stud. appl. Math. 92, 249 (1994) · Zbl 0813.76091
[19]He, J. H.: An elementary introduction of recently developed asymptotic methods and nanomechanics in textile engineering, Internat. J. Modern phys. B 22, No. 21, 3487-4578 (2008) · Zbl 1149.76607 · doi:10.1142/S0217979208048668
[20]He, J. H.; Lee, E. W. M.: A constrained variational principle for heat conduction, Phys. lett. A 373, 2614-2615 (2009) · Zbl 1231.35087 · doi:10.1016/j.physleta.2009.05.039