Ufa Mathematical Journal
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


Ufimsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find




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

Ufa Mathematical Journal, 2021, Volume 13, Issue 2, Pages 81–98
DOI: https://doi.org/10.13108/2021-13-2-81 (Mi ufa566) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy

A. O. Smirnova, V. B. Matveevb

a Saint-Petersburg State University of Aerospace Instrumentation
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
English version PDF (525 kB) Citations (5)
References:
PDF
HTML
DOI: https://doi.org/10.13108/2021-13-2-81
Abstract: Nonlinear nonlocal models exist in many fields of physics. The most known of them are models possessing $\mathcal{PT}$-symmetries. Apart of $\mathcal{PT}$-symmetric models, nonlocal models with inverse time and/or coordinates are actively studied. Other types of nonlocalities arise much rare. As a rule, in works devoted to nonlinear nonlocal equations, soliton or quasi-rational solutions to such equations are studied.
In the present work we consider nonlocal symmetries, to which all equations in the Ablowitz-Kaup-Newell-Segur hierarchy. On the base of the properties of solutions satisfying nonlocal reductions of the equations in the Ablowitz-Kaup-Newell-Segur hierarchy, we propose a modification of theta-functional formula for Baker-Akhiezer functions. We find the conditions for the parameters of spectral curves associated with multi-phase solutions possessing no exponential growth at infinity. We show that under these conditions, the variables separate. The most part of statement of our work remain true for soliton and quasi-rational solutions since they are limiting cases for the multi-phase solutions.
Keywords: nonlinear Schrödinger equation, Ablowitz-Kaup-Newell-Segur hierarchy, nonlocal equation, PT-symmetry, finite-gap solution, spectral curve, theta function.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00734
Ministry of Science and Higher Education of the Russian Federation FSRF-2020-0004
The research is supported by RFBR (grant no. 19-01-00734) and the Ministry of Science and Higher Education of Russian Federation (agreement no. FSRF-2020-0004).
Received: 15.03.2021
Russian version:
Ufimskii Matematicheskii Zhurnal, 2021, Volume 13, Issue 2, Pages 86–103
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: 37K10, 35Q55, 35Q60
Language: English
Original paper language: Russian
Citation: A. O. Smirnov, V. B. Matveev, “Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy”, Ufimsk. Mat. Zh., 13:2 (2021), 86–103; Ufa Math. J., 13:2 (2021), 81–98
Citation in format AMSBIB
\Bibitem{SmiMat21}
\by A.~O.~Smirnov, V.~B.~Matveev
\paper Finite-gap solutions of nonlocal equations in Ablowitz-Kaup-Newell-Segur hierarchy
\jour Ufimsk. Mat. Zh.
\yr 2021
\vol 13
\issue 2
\pages 86--103
\mathnet{http://mi.mathnet.ru/ufa566}
\transl
\jour Ufa Math. J.
\yr 2021
\vol 13
\issue 2
\pages 81--98
\crossref{https://doi.org/10.13108/2021-13-2-81}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000678396900008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85111730808}
Linking options:
  • https://www.mathnet.ru/eng/ufa566
  • https://doi.org/10.13108/2021-13-2-81
  • https://www.mathnet.ru/eng/ufa/v13/i2/p86
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		�������� �������������� ������
    Statistics & downloads:
    Abstract page:160
    Russian version PDF:81
    English version PDF:15
    References:22
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024