Two-gap elliptic solutions of the~Boussinesq equation
Sbornik. Mathematics, Tome 190 (1999) no. 5, pp. 763-781
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Two-gap solutions of the Boussinesq equation are considered. It is shown that for almost every Riemann surface $\Gamma$ of genus $g=2$ covering the elliptic surface it is possible to construct an elliptic (in $x$) two-gap solution of the Boussinesq equation. The existence of third- and fourth-order differential operators with elliptic “two-gap” potentials having an arbitrary number of poles is also established. An example is given.
@article{SM_1999_190_5_a4,
author = {A. O. Smirnov},
title = {Two-gap elliptic solutions of {the~Boussinesq} equation},
journal = {Sbornik. Mathematics},
pages = {763--781},
publisher = {mathdoc},
volume = {190},
number = {5},
year = {1999},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1999_190_5_a4/}
}
A. O. Smirnov. Two-gap elliptic solutions of the~Boussinesq equation. Sbornik. Mathematics, Tome 190 (1999) no. 5, pp. 763-781. http://geodesic.mathdoc.fr/item/SM_1999_190_5_a4/