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 explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. (English) Zbl 0969.76518
Summary: Based upon the well-known Riccati equation, a new generalized transformation is presented and applied to solve Whitham-Broer-Kaup (WBK) equation in shallow water. As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained. And variant Boussinesq equation and the system of approximate equation for long water waves, as the special cases of WBK equation, can also obtain the corresponding solitary wave solutions and periodic wave solutions. In addition, with the aid of Mathematica and Wu elimination method to solve a large system of algebraic equations, the course of solving equations can be carried out in computer.

MSC:
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25Solitary waves (inviscid fluids)
35L05Wave equation (hyperbolic PDE)