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)
Integrable couplings of soliton equations by perturbations. I: A general theory and application to the KdV hierarchy. (English) Zbl 1001.37061
The author discusses a problem of integrable couplings. That is, having an integrable system of evolution equations $u_t=K(u)$, how to obtain a bigger (nontrivial) integrable system consisting of $u_t=K(u)$ and $v_t = S(u,v)$. “Using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter” the author developes “a theory for constructing integrable couplings of soliton equations”. Application of the theory to the KdV hierarchy is given.

37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K40Soliton theory, asymptotic behavior of solutions
35Q53KdV-like (Korteweg-de Vries) equations