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)
On explicitly solvable Vekua equations and explicit solution of the stationary Schrödinger equation and of the equation div(σu)=0. (English) Zbl 1122.30029
There is the well-known relation in complex analysis-between holomorphic functions and pairs of conjugate harmonic functions. The authors are interested to describe generalizations of this relation, namely between solutions from special classes of Vekua’s equation and pairs of associated stationary Schrödinger equations in 2-d with potentials. If (w 1 ,w 2 ) is such a pair of solutions of associated Schrödinger equations, then w=w 1 +iw 2 represents a solution of a special Vekua equation and vice versa. It is shown that such a relation can be generalized to solutions of associated pairs of equations ·(a 1 (x,y)w 1 )=0 and ·(a 2 (x,y)w 2 )=0 in the above described sense. If w 1 is given, then the construction of w 2 is proposed. Finally, the authors discuss the question if from the explicit solvability of one Vekua equation the explicit solvability of other ones can be concluded.
MSC:
30G20Generalizations of analytic functions of Bers or Vekua type
35J10Schrödinger operator