Abel's theorem and Bäcklund transformations for the Hamilton-Jacobi equations

DOI10.1134/S0081543816080162zbMath1377.37087MaRDI QIDQ521556

Andreĭ Vladimirovich Tsyganov

Publication date: 11 April 2017

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hamilton-Jacobi equationsBäcklund transformationAbel differential equationAbel map

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relationships between algebraic curves and integrable systems (14H70) Hamilton-Jacobi equations in mechanics (70H20) Integrable cases of motion in rigid body dynamics (70E40) Hamilton-Jacobi equations (35F21)

Related Items (3)

Bäcklund transformations for the nonholonomic Veselova system ⋮ Bäcklund transformations for the Jacobi system on an ellipsoid ⋮ Duffing Oscillator and Elliptic Curve Cryptography

Cites Work

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• On auto and hetero Bäcklund transformations for the Hénon-Heiles systems
• Bäcklund transformations relating different Hamilton-Jacobi equations
• Bäcklund transformations for the Kirchhoff top
• On integrability of Hirota-Kimura type discretizations
• Integrable systems on the sphere associated with genus three algebraic curves
• Killing tensors with nonvanishing Haantjes torsion and integrable systems
• The problem of integrable discretization: Hamiltonian approach
• A new integrable system on the sphere
• Bäcklund transformations for finite-dimensional integrable systems: a geometric approach.
• On the Chaplygin system on the sphere with velocity dependent potential
• Simultaneous separation for the Neumann and Chaplygin systems
• Equivalence relations on algebraic curves
• Discretization of the Euler Top
• Non-holonomic dynamics and Poisson geometry
• Algebraic entropy for algebraic maps
• On natural Poisson bivectors on the sphere
• On bi-Hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion
• The analogue of the Backlund transformation for integrable many-body systems
• On Bäcklund transformations for many-body systems
• Separation of variables and Bäcklund transformations for the symmetric Lagrange top
• On a family of integrable systems on S² with a cubic integral of motion
• On the Routh sphere problem
• Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion

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