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)
The (G ' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. (English) Zbl 1217.76023
Summary: The (G ' G)-expansion method is firstly proposed, where G=G(ξ) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained. When the parameters are taken as special values the solitary waves are also derived from the travelling waves. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The proposed method is direct, concise, elementary and effective, and can be used for many other nonlinear evolution equations.

MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25Solitary waves (inviscid fluids)
35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations