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

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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{TM_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 = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {7--22},
     publisher = {mathdoc},
     volume = {302},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_302_a0/}
}
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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. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 7-22. http://geodesic.mathdoc.fr/item/TM_2018_302_a0/