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Mat. Sb., 1999, Volume 190, Number 5, Pages 139–157 (Mi msb405)  

This article is cited in 4 scientific papers (total in 4 papers)

Two-gap elliptic solutions of the Boussinesq equation

A. O. Smirnov

Saint-Petersburg State University of Aerospace Instrumentation

Abstract: 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.

DOI: https://doi.org/10.4213/sm405

Full text: PDF file (309 kB)
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English version:
Sbornik: Mathematics, 1999, 190:5, 763–781

Bibliographic databases:

UDC: 517.95
MSC: Primary 35Q58; Secondary 35Q53, 58F07
Received: 20.04.1998

Citation: A. O. Smirnov, “Two-gap elliptic solutions of the Boussinesq equation”, Mat. Sb., 190:5 (1999), 139–157; Sb. Math., 190:5 (1999), 763–781

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Brezhnev Yu.V., “Elliptic solitons with free constants and their isospectral deformations”, Rep. Math. Phys., 48:1-2 (2001), 39–46  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    2. Brezhnev Yu.V., “Elliptic solitons and Gröbner bases”, J. Math. Phys., 45:2 (2004), 696–712  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    3. Evgeniy Gennadievich Amosenok, Aleksandr Olegovich Smirnov, “Two-Gap Two-Elliptic Solution of Boussinesq Equation”, Lett Math Phys, 2010  crossref  mathscinet  isi  scopus  scopus  scopus
    4. A. O. Smirnov, G. M. Golovachev, E. G. Amosenok, “Dvukhzonnye 3-ellipticheskie resheniya uravnenii Bussineska i Kortevega–de Friza”, Nelineinaya dinam., 7:2 (2011), 239–256  mathnet  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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