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)
Long-time behavior of solution for coupled Ginzburg-Landau equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities. (English) Zbl 1181.35271
Summary: The Cauchy problem of coupled Ginzburg-Landau (GL) equations describing Bose-Einstein condensates and nonlinear optical waveguides and cavities is considered. The long-time behavior of solution is investigated using a series of sharp a priori estimates in phase space ${E}_{1}$ and ${E}_{2}$, respectively. The global strong attractor in ${E}_{2}$ is proved by energy equation method, and its bound of dimension is shown.
MSC:
 35Q56 Ginzburg-Landau equations 81V80 Applications of quantum theory to quantum optics 78A10 Physical optics 35B40 Asymptotic behavior of solutions of PDE 35B45 A priori estimates for solutions of PDE 35B41 Attractors (PDE)