RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2018, Volume 302, Pages 7–22 (Mi tm3924)  

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

Real soliton lattices of the Kadomtsev–Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case

Simonetta Abendaa, Petr G. Grinevichbc

a Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna (BO), Italy
b L.D. Landau Institute for Theoretical Physics of Russian Academy of Sciences, pr. Ak. Semenova 1a, Chernogolovka, Moscow oblast, 142432 Russia
c Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia

Abstract: We apply the general construction developed in our previous papers to the first nontrivial case of $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$. In particular, we construct finite-gap real quasi-periodic solutions of the KP-II equation in the form of a soliton lattice corresponding to a smooth $\mathtt M$-curve of genus $4$ which is a desingularization of a reducible rational $\mathtt M$-curve for soliton data in $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$.

Funding Agency Grant Number
Istituto Nazionale di Alta Matematica "Francesco Severi"
Russian Academy of Sciences - Federal Agency for Scientific Organizations 0033-2018-0009
Russian Foundation for Basic Research 17-01-00366-а
This research was partially supported by the GNFM-INdAM and RFO University of Bologna. The research of the second author was performed in part within the framework of the state assignment of FASO Russia (theme “Mathematical physics,” no. 0033-2018-0009) and was supported in part by the Russian Foundation for Basic Research (project no. 17-01-00366-a).


DOI: https://doi.org/10.1134/S0371968518030019

Full text: PDF file (956 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 302, 1–15

Bibliographic databases:

UDC: 517.958
Received: April 23, 2018

Citation: Simonetta Abenda, Petr G. Grinevich, “Real soliton lattices of the Kadomtsev–Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case”, Topology and physics, Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 7–22; Proc. Steklov Inst. Math., 302 (2018), 1–15

Citation in format AMSBIB
\Bibitem{AbeGri18}
\by Simonetta~Abenda, Petr~G.~Grinevich
\paper Real soliton lattices of the Kadomtsev--Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case
\inbook Topology and physics
\bookinfo Collected papers. Dedicated to Academician Sergei Petrovich Novikov on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2018
\vol 302
\pages 7--22
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3924}
\crossref{https://doi.org/10.1134/S0371968518030019}
\elib{http://elibrary.ru/item.asp?id=36503429}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2018
\vol 302
\pages 1--15
\crossref{https://doi.org/10.1134/S0081543818060019}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454896300001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059522279}


Linking options:
  • http://mi.mathnet.ru/eng/tm3924
  • https://doi.org/10.1134/S0371968518030019
  • http://mi.mathnet.ru/eng/tm/v302/p7

    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

    This publication is cited in the following articles:
    1. Atsushi Nakayashiki, “On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions”, SIGMA, 15 (2019), 009, 18 pp.  mathnet  crossref
    2. Abenda S., Grinevich P.G., “Reducible M-Curves For Le-Networks in the Totally-Nonnegative Grassmannian and Kp-II Multiline Solitons”, Sel. Math.-New Ser., 25:3 (2019), UNSP 43  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:163
    References:10
    First page:15

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020