Geodesic
Real soliton lattices of the Kadomtsev--Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case
Informatics and Automation, Topology and physics, Tome 302 (2018), pp. 7-22

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$. 
@article{TRSPY_2018_302_a0,
     author = {Simonetta Abenda and Petr G. Grinevich},
     title = {Real soliton lattices of the {Kadomtsev--Petviashvili} {II} equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case},
     journal = {Informatics and Automation},
     pages = {7--22},
     publisher = {mathdoc},
     volume = {302},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_302_a0/}
}
TY  - JOUR
AU  - Simonetta Abenda
AU  - Petr G. Grinevich
TI  - Real soliton lattices of the Kadomtsev--Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case
JO  - Informatics and Automation
PY  - 2018
SP  - 7
EP  - 22
VL  - 302
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2018_302_a0/
LA  - ru
ID  - TRSPY_2018_302_a0
ER  - 
%0 Journal Article
%A Simonetta Abenda
%A Petr G. Grinevich
%T Real soliton lattices of the Kadomtsev--Petviashvili II equation and desingularization of spectral curves: the $\mathrm {Gr^{ \scriptscriptstyle TP}}(2,4)$ case
%J Informatics and Automation
%D 2018
%P 7-22
%V 302
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2018_302_a0/
%G ru
%F TRSPY_2018_302_a0
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. Informatics and Automation, Topology and physics, Tome 302 (2018), pp. 7-22. http://geodesic.mathdoc.fr/item/TRSPY_2018_302_a0/