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, Trudy Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 7–22; Proc. Steklov Inst. Math., 302 (2018), 1

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 302, Pages 7–22
DOI: https://doi.org/10.1134/S0371968518030019 (Mi tm3924)

This article is cited in 9 scientific papers (total in 9 papers)

Real soliton lattices of the Kadomtsev–Petviashvili II equation and desingularization of spectral curves: the

G r^{T P} (2, 4)

$\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case

Simonetta Abenda^a, Petr G. Grinevich^bc

^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

Full-text PDF (956 kB) Citations (9)

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

Abstract: We apply the general construction developed in our previous papers to the first nontrivial case of

G r^{T P} (2, 4)

$\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ . 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).

Received: April 23, 2018

English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 302, Pages 1–15
DOI: https://doi.org/10.1134/S0081543818060019

Bibliographic databases:

Document Type: Article

UDC: 517.958

Language: Russian

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, Trudy Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 7–22; Proc. Steklov Inst. Math., 302 (2018), 1–15

Citation in format AMSBIB

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\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 Trudy Mat. Inst. Steklova

\yr 2018

\vol 302

\pages 7--22

\publ MAIK Nauka/Interperiodica

\publaddr Moscow

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Linking options:

https://www.mathnet.ru/eng/tm3924

https://doi.org/10.1134/S0371968518030019

https://www.mathnet.ru/eng/tm/v302/p7

This publication is cited in the following 9 articles:

Gino Biondini, Alexander J Bivolcic, Mark A Hoefer, Antonio Moro, “Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation”, Nonlinearity, 37:2 (2024), 025012
Atsushi Nakayashiki, “Vertex operators of the KP hierarchy and singular algebraic curves”, Lett Math Phys, 114:3 (2024)
P. G. Grinevich, S. Abenda, “Geometric nature of relations on plabic graphs and totally non-negative Grassmannians”, Int. Math. Res. Not. IMRN, 2023:14 (2023), 11986–12051
P. G. Grinevich, S. Abenda, “Real regular KP divisors on 𝙼-curves and totally non-negative Grassmannians”, Lett. Math. Phys., 112 (2022), 115–64
P. G. Grinevich, S. Abenda, “Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians”, Adv. Math., 406 (2022), 108523–57
S. Abenda, “Kasteleyn theorem, geometric signatures and kp-ii divisors on planar bipartite networks in the disk”, Math. Phys. Anal. Geom., 24:4 (2021), 35
D. Wu, “The direct scattering problem for perturbed Kadomtsev-Petviashvili multi line solitons”, J. Math. Phys., 62:9 (2021), 091513
Atsushi Nakayashiki, “On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions”, SIGMA, 15 (2019), 009, 18 pp.
S. Abenda, P. G. Grinevich, “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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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