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)
The inverse scattering transform and squared eigenfunctions for a degenerate $3 \times 3$ operator. (English) Zbl 1178.35382
Summary: We present the covering set of the squared eigenfunctions for a degenerate $3 \times 3$ eigenvalue problem. The derivation follows the approach recently outlined by us on this same equation [J. Math. Phys. 50, No. 2, Paper No. 023504 (2009; Zbl 1202.35275)]. This eigenvalue problem is important since it serves as the spectral problem for the inverse scattering transform (IST) of the vector NLS equation, the Sasa-Satsuma equation, and a degenerate two-level Maxwell-Bloch system. The use of this covering set allows one to treat the linear perturbations of these equations in a common and systematic manner. Comparison with previous results on the perturbed continuous spectrum of the Sasa-Satsuma equation is made.

35R30Inverse problems for PDE
35P25Scattering theory (PDE)
81U40Inverse scattering problems (quantum theory)
Full Text: DOI