Abstract:
An ansatz concerning Krichever curves is considered for two-periodic finite-gap solutions of the Boussinesq equation. These solutions are expressed in terms of equianharmonic elliptic Weierstrass ℘-functions. Examples are given.
Citation:
A. O. Smirnov, “On some set of elliptic solutions of the Boussinesq equation”, TMF, 109:3 (1996), 347–356; Theoret. and Math. Phys., 109:3 (1996), 1515–1522
\Bibitem{Smi96}
\by A.~O.~Smirnov
\paper On some set of elliptic solutions of the Boussinesq equation
\jour TMF
\yr 1996
\vol 109
\issue 3
\pages 347--356
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\crossref{https://doi.org/10.4213/tmf1232}
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\transl
\jour Theoret. and Math. Phys.
\yr 1996
\vol 109
\issue 3
\pages 1515--1522
\crossref{https://doi.org/10.1007/BF02073868}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996XN86800003}
Linking options:
https://www.mathnet.ru/eng/tmf1232
https://doi.org/10.4213/tmf1232
https://www.mathnet.ru/eng/tmf/v109/i3/p347
This publication is cited in the following 4 articles:
Geng X., Wu L., He G., “Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions”, Physica D-Nonlinear Phenomena, 240:16 (2011), 1262–1288
A. O. Smirnov, “Two-gap elliptic solutions of the Boussinesq equation”, Sb. Math., 190:5 (1999), 763–781
Dickson, R, “Algebro-geometric solutions of the Boussinesq hierarchy”, Reviews in Mathematical Physics, 11:7 (1999), 823
Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271