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 tanh method for traveling wave solutions of nonlinear equations. (English) Zbl 1054.65106
Summary: We employ the tanh method for traveling wave solutions of nonlinear equations. The study is extended to equations that do not have tanh polynomial solutions. The efficiency of the method is demonstrated by applying it for a variety of selected equations.

65M70Spectral, collocation and related methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations
Full Text: DOI
[1] Malfliet, W.: Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60, No. 7, 650-654 (1992) · Zbl 1219.35246
[2] Malfliet, W.: The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Physica scripta 54, 563-568 (1996) · Zbl 0942.35034
[3] Malfliet, W.: The tanh method: II. Perturbation technique for conservative systems. Physica scripta 54, 569-575 (1996) · Zbl 0942.35035
[4] Khater, A. H.; Malfliet, W.; Callebaut, D. K.; Kamel, E. S.: The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction--diffusion equations. Chaos soliton. Fract. 14, 513-522 (2002) · Zbl 1002.35066
[5] Parkes, E. J.; Duffy, B. R.: An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Comput. phys. Commun. 98, 288-300 (1996) · Zbl 0948.76595
[6] Fan, E.; Hon, Y. C.: Generalized tanh method extended to special types of nonlinear equations. Z. naturforsch 57a, 692-700 (2002)
[7] Glasner, K.: Nonlinear preconditioning for diffuse interfaces. J. comput. Phys. 174, 695-711 (2001) · Zbl 0991.65076
[8] Kawahara, T.; Tanaka, M.: Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation. Phys. lett. 97A, No. 8, 311-314 (1983)
[9] Conte, R.; Mussette, M.: Link between solitary waves and projective Riccati equations. J. phys.: math. Gen. 25, 5609-5623 (1992) · Zbl 0782.35065
[10] Huibin, L.; Kelin, W.: Exact solutions for two nonlinear equations: I. J. phys. A: math. Gen. 23, 3923-3928 (1990) · Zbl 0718.35020
[11] Wang, M.: Exact solutions for a compound KdV--Burgers equation. Phys. lett. A 213, 279-287 (1998) · Zbl 0972.35526
[12] Ma, W.: Travelling wave solutions to a seventh order generalized KdV equation. Phys. lett. A 180, 221-224 (1993)
[13] Wazwaz, A. M.: Partial differential equations: methods and applications. (2002) · Zbl 1079.35001