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Mathematics of the USSR-Izvestiya, 1990, Volume 35, Issue 3, Pages 629–655
DOI: https://doi.org/10.1070/IM1990v035n03ABEH000720 (Mi im1157) 		 
This article is cited in 39 scientific papers (total in 39 papers)

Commuting differential operators of rank 3, and nonlinear differential equations

O. I. Mokhov
English version PDF (1146 kB) Citations (39)
References:
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DOI: https://doi.org/10.1070/IM1990v035n03ABEH000720
Abstract: Complete solutions of the commutation equations of ordinary differential operators are obtained, to which there corresponds a three-dimensional vector bundle of common eigenfunctions over an elliptic curve. The deformation of the commuting pair by the Kadomtsev–Petviashvili equation is studied. The finite-zone solutions of the Kadomtsev–Petviashvili equation of rank 3 and genus 1 are explicitly expressed in terms of functional parameters satisfying a Boussinesq-type system of two evolution equations.
Bibliography: 40 titles.
Received: 27.04.1988
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1989, Volume 53, Issue 6, Pages 1291–1315
Bibliographic databases:
UDC: 517.9+512.7
MSC: Primary 47E05, 14K07, 14K25; Secondary 25D25, 34B25, 58F37, 14G10, 12F10
Language: English
Original paper language: Russian
Citation: O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989), 1291–1315; Math. USSR-Izv., 35:3 (1990), 629–655
Citation in format AMSBIB
\Bibitem{Mok89}
\by O.~I.~Mokhov
\paper Commuting differential operators of rank~3, and nonlinear differential equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 6
\pages 1291--1315
\mathnet{http://mi.mathnet.ru/im1157}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1039965}
\zmath{https://zbmath.org/?q=an:0707.34009}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 3
\pages 629--655
\crossref{https://doi.org/10.1070/IM1990v035n03ABEH000720}
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  • https://www.mathnet.ru/eng/im/v53/i6/p1291
    • This publication is cited in the following 39 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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    Abstract page:902
    Russian version PDF:301
    English version PDF:20
    References:85
    First page:3
     
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