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)
Inverse scattering solutions of the Hunter-Saxton equation. (English) Zbl 1020.35092
Summary: The nonlinear partial differential equation $(u_t+ uu_x)_{xx}= {1\over 2}(u^2_x)_x$ was proposed by Hunter and Saxton as an asymptotic model equation for nematic liquid crystals. Hunter and Zheng showed that it is a member of the Harry Dym hierarchy of integrable flows, and solved the equation explicitly for a family of finite-dimensional, piecewise linear functions in the case when $u_x$ has compact support. In this note, the associated inverse scattering problem is used to obtain the explicit solutions of the finite-dimensional flows in both the compact and non-compact case.

35Q53KdV-like (Korteweg-de Vries) equations
37K15Integration of completely integrable systems by inverse spectral and scattering methods
35C10Series solutions of PDE
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q51Soliton-like equations
35P20Asymptotic distribution of eigenvalues and eigenfunctions for PD operators
35P25Scattering theory (PDE)
Full Text: DOI