RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Mat. Fiz. Anal. Geom.:
Year:
Volume:
Issue:
Page:
Find






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


Zh. Mat. Fiz. Anal. Geom., 2018, Volume 14, Number 4, Pages 406–451 (Mi jmag706)  

Long-time asymptotics for the Toda shock problem: non-overlapping spectra

Iryna Egorovaa, Johanna Michorb, Gerald Teschlb

a B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
b Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

Abstract: We derive the long-time asymptotics for the Toda shock problem using the nonlinear steepest descent analysis for oscillatory Riemann–Hilbert factorization problems. We show that the half-plane of space/time variables splits into five main regions: The two regions far outside where the solution is close to the free backgrounds. The middle region, where the solution can be asymptotically described by a two band solution, and two regions separating them, where the solution is asymptotically given by a slowly modulated two band solution. In particular, the form of this solution in the separating regions verifies a conjecture from Venakides, Deift, and Oba from 1991.

Key words and phrases: Toda lattice, Riemann–Hilbert problem, shock wave.

Funding Agency Grant Number
Austrian Science Fund Y330
V120
Research supported by the Austrian Science Fund (FWF) under Grants No. Y330, V120, and by the grant ”Network of Mathematical Research 2013–2015”.


DOI: https://doi.org/10.15407/mag14.04.406

Full text: PDF file (1055 kB)
References: PDF file   HTML file

Document Type: Article
MSC: Primary 37K40, 37K10; Secondary 37K60, 35Q15
Received: 06.01.2018
Language: English

Citation: Iryna Egorova, Johanna Michor, Gerald Teschl, “Long-time asymptotics for the Toda shock problem: non-overlapping spectra”, Zh. Mat. Fiz. Anal. Geom., 14:4 (2018), 406–451

Citation in format AMSBIB
\Bibitem{EgoMicTes18}
\by Iryna~Egorova, Johanna~Michor, Gerald~Teschl
\paper Long-time asymptotics for the Toda shock problem: non-overlapping spectra
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2018
\vol 14
\issue 4
\pages 406--451
\mathnet{http://mi.mathnet.ru/jmag706}
\crossref{https://doi.org/10.15407/mag14.04.406}


Linking options:
  • http://mi.mathnet.ru/eng/jmag706
  • http://mi.mathnet.ru/eng/jmag/v14/i4/p406

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:13
    Full text:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019