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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 2, Pages 12–27 (Mi faa104)  

This article is cited in 17 scientific papers (total in 17 papers)

Heat Equations in a Nonholonomic Frame

V. M. Buchstabera, D. V. Leikinb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Magnetism, National Academy of Sciences of Ukraine

Abstract: A system of heat equations in a nonholonomic frame is considered. Solutions of the system are constructed in the form of general sigma functions of Abelian tori. As a corollary, we solve the problem (of general interest) to describe the generators of the ring of differential operators annihilating the sigma functions of families of plane algebraic curves.

Keywords: nonholonomic frame, heat equations, sigma and theta functions in several variables, discriminant varieties


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English version:
Functional Analysis and Its Applications, 2004, 38:2, 88–101

Bibliographic databases:

UDC: 517.958+515.178.2
Received: 09.02.2004

Citation: V. M. Buchstaber, D. V. Leikin, “Heat Equations in a Nonholonomic Frame”, Funktsional. Anal. i Prilozhen., 38:2 (2004), 12–27; Funct. Anal. Appl., 38:2 (2004), 88–101

Citation in format AMSBIB
\by V.~M.~Buchstaber, D.~V.~Leikin
\paper Heat Equations in a Nonholonomic Frame
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 2
\pages 12--27
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 2
\pages 88--101

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    This publication is cited in the following articles:
    1. V. M. Buchstaber, D. V. Leikin, “Addition Laws on Jacobian Varieties of Plane Algebraic Curves”, Proc. Steklov Inst. Math., 251 (2005), 49–120  mathnet  mathscinet  zmath
    2. Buchstaber V., Leykin D., “Hyperelliptic addition law”, J. Nonlinear Math. Phys., 12, suppl. 1 (2005), 106–123  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. V. M. Buchstaber, D. V. Leikin, “Differentiation of Abelian functions with respect to parameters”, Russian Math. Surveys, 62:4 (2007), 787–789  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. V. M. Buchstaber, D. V. Leikin, “Solution of the Problem of Differentiation of Abelian Functions over Parameters for Families of $(n,s)$-Curves”, Funct. Anal. Appl., 42:4 (2008), 268–278  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. E. Yu. Bunkova, V. M. Buchstaber, “Heat Equations and Families of Two-Dimensional Sigma Functions”, Proc. Steklov Inst. Math., 266 (2009), 1–28  mathnet  crossref  mathscinet  zmath  isi  elib
    6. Buchstaber V.M., “Heat Equations and Sigma Functions”, Geometric Methods in Physics, AIP Conference Proceedings, 1191, 2009, 46–58  crossref  adsnasa  isi  scopus
    7. E. Yu. Netay, “Geometric differential equations on bundles of Jacobians of curves of genus 1 and 2”, Trans. Moscow Math. Soc., 74 (2013), 281–292  mathnet  crossref  mathscinet  zmath  elib
    8. V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. Julia Bernatska, Dmitry Leykin, “On Regularization of Second Kind Integrals”, SIGMA, 14 (2018), 074, 28 pp.  mathnet  crossref
    10. Onishi Y., “Arithmetical Power Series Expansion of the SIGMA Function For a Plane Curve”, Proc. Edinb. Math. Soc., 61:4 (2018), 995–1022  crossref  mathscinet  isi  scopus
    11. Bernatska J. Leykin D., “On Degenerate SIGMA-Functions in Genus 2”, Glasg. Math. J., 61:1 (2019), 169–193  crossref  mathscinet  zmath  isi
    12. A. V. Domrin, “Uniqueness theorem for the two-dimensional sigma function”, Funct. Anal. Appl., 54:1 (2020), 21–30  mathnet  crossref  crossref  mathscinet  isi  elib
    13. V. M. Buchstaber, E. Yu. Bunkova, “Lie Algebras of Heat Operators in a Nonholonomic Frame”, Math. Notes, 108:1 (2020), 15–28  mathnet  crossref  crossref  mathscinet  isi  elib
    14. V. M. Buchstaber, E. Yu. Bunkova, “Sigma Functions and Lie Algebras of Schrödinger Operators”, Funct. Anal. Appl., 54:4 (2020), 229–240  mathnet  crossref  crossref  mathscinet  isi  elib
    15. Julia Bernatska, Yaacov Kopeliovich, “Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials”, SIGMA, 16 (2020), 053, 21 pp.  mathnet  crossref
    16. T. Ayano, V. M. Buchstaber, “Analytical and number-theoretical properties of the two-dimensional sigma function”, Chebyshevskii sb., 21:1 (2020), 9–50  mathnet  crossref  mathscinet
    17. V. M. Bukhshtaber, E. Yu. Bunkova, “Giperellipticheskie sigma-funktsii i polinomy Adlera–Mozera”, Funkts. analiz i ego pril., 55:3 (2021), 3–25  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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