Algebra i Analiz
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Analiz, 1994, Volume 6, Issue 3, Pages 40–58 (Mi aa450)  

This article is cited in 2 scientific papers (total in 2 papers)

Research Papers

On some developments of the $\overline\partial$-dressing method

L. V. Bogdanov, V. E. Zakharov

Landau Institute for Theoretical Physics, Centre for Non-linear Studies
Abstract: Some developments of the $\overline\partial$-dressing method concerning an algebraic scheme of constructing integrable equations and construction of solutions with special properties are considered. It is demonstrated how the matrix $\mathbf{KP}$ equation appears from the scalar dressing and, more generally, how to construct the integrable system corresponding to an arbitrary triad of polynomials. Using the nonlocal $\overline\partial$-problem approach in $(2+1)$ dimensions, it is shown that the $\overline\partial$-problem with a shift and (for decreasing solutions) the Riemann problem with a shift naturally arise in $(1+1)$ dimensions. The Boussinesq equation and the first order relativistically-invariant systems are investigated. The developed approach allows one also to investigate the structure of the continuous spectrum and the inverse scattering problem for an arbitrary order ordinary differential operator on the infinite line.
Keywords: Inverse scattering problem method, the dressing method, $\bar\partial$-problem, the Riemann problem.
Received: 13.04.1994
Bibliographic databases:
Document Type: Article
Language: English
Citation: L. V. Bogdanov, V. E. Zakharov, “On some developments of the $\overline\partial$-dressing method”, Algebra i Analiz, 6:3 (1994), 40–58; St. Petersburg Math. J., 6:3 (1995), 475–493
Citation in format AMSBIB
\Bibitem{BogZak94}
\by L.~V.~Bogdanov, V.~E.~Zakharov
\paper On some developments of the $\overline\partial$-dressing method
\jour Algebra i Analiz
\yr 1994
\vol 6
\issue 3
\pages 40--58
\mathnet{http://mi.mathnet.ru/aa450}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1301829}
\zmath{https://zbmath.org/?q=an:0839.35115|0813.35102}
\transl
\jour St. Petersburg Math. J.
\yr 1995
\vol 6
\issue 3
\pages 475--493
Linking options:
  • https://www.mathnet.ru/eng/aa450
  • https://www.mathnet.ru/eng/aa/v6/i3/p40
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
    Statistics & downloads:
    Abstract page:455
    Full-text PDF :164
    References:1
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024