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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 $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ 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 $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$.
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, Trudy Mat. Inst. Steklova, 302, MAIK Nauka/Interperiodica, Moscow, 2018, 7–22; Proc. Steklov Inst. Math., 302 (2018), 1–15
Linking options:
https://www.mathnet.ru/eng/tm3924https://doi.org/10.1134/S0371968518030019 https://www.mathnet.ru/eng/tm/v302/p7
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