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

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-à 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

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

Bibliographic databases:

UDC: 517.958

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} 

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

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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.
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
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