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)
The extended tanh method for the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms. (English) Zbl 1221.35373
Summary: The reliable extended tanh method, that combines tanh with coth, is used for analytic treatment of the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and the generalized forms of these equations. New travelling wave solutions with solitons and periodic structures are determined. The power of the employed method is confirmed.
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
[1]Monro, S.; Parkes, E. J.: The derivation of a modified Zakharov – Kuznetsov equation and the stability of its solutions, J plasma phys 62, No. 3, 305-317 (1999)
[2]Monro, S.; Parkes, E. J.: Stability of solitary-wave solutions to a modified Zakharov – Kuznetsov equation, J plasma phys 64, No. 3, 411-426 (2000)
[3]Schamel, H.: A modified Korteweg – de-Vries equation for ion acoustic waves due to resonant electrons, J plasma phys 9, No. 3, 377-387 (1973)
[4]Ablowitz, M. J.; Clarkson, P. A.: Solitons, nonlinear evolution equations and inverse scattering, (1991) · Zbl 0762.35001
[5]Wadati, M.: The exact solution of the modified kortweg – de Vries equation, J phys soc jpn 32, 1681-1687 (1972)
[6]Li, B.; Chen, Y.; Zhang, H.: Exact travelling wave solutions for a generalized Zakharov – Kuznetsov equation, Appl math comput 146, 653-666 (2003) · Zbl 1037.35070 · doi:10.1016/S0096-3003(02)00610-0
[7]Kadomtsev, B. B.; Petviashvili, V. I.: Sov phys JETP, Sov phys JETP 39, 285-295 (1974)
[8]Zakharov, V. E.; Kuznetsov, E. A.: On three-dimensional solitons, Sov phys 39, 285-288 (1974)
[9]Shivamoggi, B. K.: The Painlevé analysis of the Zakharov – Kuznetsov equation, Phys scr 42, 641-642 (1990) · Zbl 1063.35550 · doi:10.1088/0031-8949/42/6/001
[10]Malfliet, W.: Solitary wave solutions of nonlinear wave equations, Am J phys 60, No. 7, 650-654 (1992) · Zbl 1219.35246 · doi:10.1119/1.17120
[11]Malfliet, W.: The tanh method: a tool for solving certain classes of nonlinear evolution and wave equations, J comput appl math 164 – 165, 529-541 (2004) · Zbl 1038.65102 · doi:10.1016/S0377-0427(03)00645-9
[12]Wazwaz, A. M.: The tanh method for generalized forms of nonlinear heat conduction and Burgers – Fisher equations, Appl math comput 169, 321-338 (2005) · Zbl 1121.65359 · doi:10.1016/j.amc.2004.09.054
[13]Wazwaz, A. M.: Nonlinear dispersive special type of the Zakharov – Kuznetsov equation ZK(n,n) with compact and noncompact structures, Appl math comput 161, 577-590 (2005) · Zbl 1061.65105 · doi:10.1016/j.amc.2003.12.050
[14]Wazwaz, A. M.: Special types of the nonlinear dispersive Zakharov – Kuznetsov equation with compactons, solitons and periodic solutions, Int J comput math 81, No. 9, 1107-1119 (2004) · Zbl 1059.35131 · doi:10.1080/00207160410001684253
[15]Wazwaz, A. M.: Exact solutions with solitons and periodic structures for the Zakharov – Kuznetsov (ZK) equation and its modified form, Commun nonlinear sci numer simul 10, 597-606 (2005) · Zbl 1070.35075 · doi:10.1016/j.cnsns.2004.03.001
[16]Wazwaz, A. M.: Partial differential equations: methods and applications, (2002)
[17]Wazwaz, A. M.: A computational approach to soliton solutions of the Kadomtsev – petviashili equation, Appl math comput 123, No. 2, 205-217 (2001) · Zbl 1024.65098 · doi:10.1016/S0096-3003(00)00065-5
[18]Wazwaz, A. .M.: An analytic study of compactons structures in a class of nonlinear dispersive equations, Math comput simul 63, No. 1, 35-44 (2003) · Zbl 1021.35092 · doi:10.1016/S0378-4754(02)00255-0
[19]Wazwaz, A. M.: Existence and construction of compacton solutions, Chaos solitons fractals 19, No. 3, 463-470 (2004) · Zbl 1068.35124 · doi:10.1016/S0960-0779(03)00171-1
[20]Wazwaz, A. M.: Compactons in a class of nonlinear dispersive equations, Math comput modell 37, No. 3/4, 333-341 (2003) · Zbl 1044.35078 · doi:10.1016/S0895-7177(03)00010-4