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

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Funktsional'nyi Analiz i ego Prilozheniya, 2004, Volume 38, Issue 2, Pages 12–27
DOI: https://doi.org/10.4213/faa104 (Mi faa104)

This article is cited in 26 scientific papers (total in 26 papers)

Heat Equations in a Nonholonomic Frame

V. M. Buchstaber^a, D. V. Leikin^b

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

Full-text PDF (276 kB) Citations (26)

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DOI: https://doi.org/10.4213/faa104

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.

Received: 09.02.2004

English version:
Functional Analysis and Its Applications, 2004, Volume 38, Issue 2, Pages 88–101
DOI: https://doi.org/10.1023/B:FAIA.0000034039.92913.8a

Bibliographic databases:

Document Type: Article

UDC: 517.958+515.178.2

Language: Russian

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

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Linking options:

https://www.mathnet.ru/eng/faa104

https://doi.org/10.4213/faa104

https://www.mathnet.ru/eng/faa/v38/i2/p12

This publication is cited in the following 26 articles:

Julia Bernatska, “Abelian Function Fields on Jacobian Varieties”, Axioms, 14:2 (2025), 90
J. Chris Eilbeck, John Gibbons, Yoshihiro Ônishi, Seidai Yasuda, “Theory of heat equations for sigma functions”, Glasgow Math. J., 2025, 1
Shigeki Matsutani, “Statistical mechanics of elastica for the shape of supercoiled DNA: Hyperelliptic elastica of genus three”, Physica A: Statistical Mechanics and its Applications, 643 (2024), 129799
V. M. Buchstaber, E. Yu. Bunkova, “Formulas for Differentiating Hyperelliptic Functions with Respect to Parameters and Periods”, Proc. Steklov Inst. Math., 325 (2024), 60–73
V. M. Buchstaber, “The Mumford dynamical system and hyperelliptic Kleinian functions”, Funct. Anal. Appl., 57:4 (2023), 288–302
E. Yu. Bunkova, V. M. Buchstaber, “Explicit Formulas for Differentiation of Hyperelliptic Functions”, Math. Notes, 114:6 (2023), 1151–1162
Julia Bernatska, Dmitry Leykin, “Solution of the Jacobi inversion problem on non-hyperelliptic curves”, Lett Math Phys, 113:5 (2023)
Takanori Ayano, Victor M. Buchstaber, “Relationships Between Hyperelliptic Functions of Genus $2$ and Elliptic Functions”, SIGMA, 18 (2022), 010, 30 pp.
V. M. Buchstaber, E. Yu. Bunkova, “Hyperelliptic Sigma Functions and Adler–Moser Polynomials”, Funct. Anal. Appl., 55:3 (2021), 179–197
A. V. Domrin, “Uniqueness theorem for the two-dimensional sigma function”, Funct. Anal. Appl., 54:1 (2020), 21–30
V. M. Buchstaber, E. Yu. Bunkova, “Lie Algebras of Heat Operators in a Nonholonomic Frame”, Math. Notes, 108:1 (2020), 15–28
V. M. Buchstaber, E. Yu. Bunkova, “Sigma Functions and Lie Algebras of Schrödinger Operators”, Funct. Anal. Appl., 54:4 (2020), 229–240
Julia Bernatska, Yaacov Kopeliovich, “Addition of Divisors on Hyperelliptic Curves via Interpolation Polynomials”, SIGMA, 16 (2020), 053, 21 pp.
T. Ayano, V. M. Buchstaber, “Analytical and number-theoretical properties of the two-dimensional sigma function”, Chebyshevskii sb., 21:1 (2020), 9–50
Buchstaber V.M. Enolski V.Z. Leykin D.V., “SIGMA-Functions: Old and New Results”, Integrable Systems and Algebraic Geometry: a Celebration of Emma Previato'S 65Th Birthday, Vol 2, London Mathematical Society Lecture Note Series, 459, ed. Donagi R. Shaska T., Cambridge Univ Press, 2020, 175–214
Bernatska J. Leykin D., “On Degenerate SIGMA-Functions in Genus 2”, Glasg. Math. J., 61:1 (2019), 169–193
Julia Bernatska, Dmitry Leykin, “On Regularization of Second Kind Integrals”, SIGMA, 14 (2018), 074, 28 pp.
Onishi Y., “Arithmetical Power Series Expansion of the SIGMA Function For a Plane Curve”, Proc. Edinb. Math. Soc., 61:4 (2018), 995–1022
V. M. Buchstaber, “Polynomial dynamical systems and the Korteweg–de Vries equation”, Proc. Steklov Inst. Math., 294 (2016), 176–200
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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