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)
Existence and uniqueness of the solution to the modified Schrödinger map. (English) Zbl 1082.35140
The author studies the initial value problem for a system of nonlinear Schrödinger equations in two space dimensions (modified Schrödinger map) which is derived from Schrödinger maps from $\bbfR\times \bbfR^2$ to the unit sphere $S^2$ or to the hyperbolic space $\bbfH^2$ by using appropriate gauge change. The existence and uniqueness of the solution was known for data in $H^s(\bbfR^2)$ with $s> 1$. In this paper the local existence of the solution is proved for the initial data in $H^s(\bbfR^2)$ with $s> 1/2$. The uniqueness of the solution is also proved when the data belong to $H^1(\bbfR^2)$.

35Q55NLS-like (nonlinear Schrödinger) equations
35G25Initial value problems for nonlinear higher-order PDE
Full Text: DOI