Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Russian Mathematical Surveys, 2008, Volume 63, Issue 6, Pages 999–1010
DOI: https://doi.org/10.1070/RM2008v063n06ABEH004575
(Mi rm9242)
 

This article is cited in 7 scientific papers (total in 7 papers)

Hamiltonian PDEs and Frobenius manifolds

B. A. Dubrovinab

a Steklov Mathematical Institute, Russian Academy of Sciences
b International School for Advanced Studies (SISSA)
References:
Abstract: In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg–de Vries, non-linear Schrödinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Received: 01.09.2008
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 53D45, 37K10
Language: English
Original paper language: Russian
Citation: B. A. Dubrovin, “Hamiltonian PDEs and Frobenius manifolds”, Russian Math. Surveys, 63:6 (2008), 999–1010
Citation in format AMSBIB
\Bibitem{Dub08}
\by B.~A.~Dubrovin
\paper Hamiltonian PDEs and Frobenius manifolds
\jour Russian Math. Surveys
\yr 2008
\vol 63
\issue 6
\pages 999--1010
\mathnet{http://mi.mathnet.ru//eng/rm9242}
\crossref{https://doi.org/10.1070/RM2008v063n06ABEH004575}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2492769}
\zmath{https://zbmath.org/?q=an:1170.53072}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2008RuMaS..63..999D}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000267769700002}
\elib{https://elibrary.ru/item.asp?id=20423393}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65649152561}
Linking options:
  • https://www.mathnet.ru/eng/rm9242
  • https://doi.org/10.1070/RM2008v063n06ABEH004575
  • https://www.mathnet.ru/eng/rm/v63/i6/p7
  • Related presentations:
    This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:1237
    Russian version PDF:447
    English version PDF:36
    References:114
    First page:39
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024