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)
Elliptic general analytic solutions. (English) Zbl 1185.35221
To find analytically the traveling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: “projective Riccati method”, “tanh-method”, “exponential method”, “Jacobi expansion method”, etc. The common default to all these “truncation methods” is that they provide only some solutions, not all of them. By implementing three classical results of Briot, Bouquet, and Poincaré they present an algorithm able to provide in closed form all those traveling waves that are elliptic or degenerate elliptic, i.e., rational in one exponential or rational. The examples in the paper are based on the Kuramoto-Sivashinsky equation and the cubic and quintic complex Ginzburg-Landau equations.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35Q56Ginzburg-Landau equations
35C07Traveling wave solutions of PDE