Simultaneous separation for the Neumann and Chaplygin systems

Abstract

The Neumann and Chaplygin systems on the sphere are simultaneously separable in variables obtained from the standard elliptic coordinates by the proper Backlund transformation. We also prove that after similar Backlund transformations other curvilinear coordinates on the sphere and on the plane become variables of separations for the system with quartic potential, for the Henon-Heiles system and for the Kowalevski top. It allows us to say about some analog of the hetero Backlund transformations relating different Hamilton-Jacobi equations.

21 pages, LaTeX with Amsfonts. arXiv admin note: text overlap with arXiv:nlin/0307021 by other authors

References in corpus (13)

• Separation of Variables. New Trends.
• Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras
• Separation of variables for the classical and quantum Neumann model
• Backlund transformations for finite-dimensional integrable systems: a geometric approach
• New variables of separation for particular case of the Kowalevski top
• On the generalized integrable Chaplygin system
• On bi-integrable natural Hamiltonian systems on the Riemannian manifolds
• On the Steklov-Lyapunov case of the rigid body motion
• Generalized Lenard Chains, Separation of Variables and Superintegrability
• Spectrum of the quantum Neumann model
• Simultaneous separation for the Kowalevski and Goryachev-Chaplygin gyrostats
• Integrable systems on the sphere associated with genus three algebraic curves
• New Variables of Separation for the Steklov-Lyapunov System

Cited by in corpus (10)

• On auto and hetero Backlund transformations for the Henon-Heiles systems
• New bi-Hamiltonian systems on the plane
• Backlund transformations and divisor doubling
• Bäcklund transformations for the nonholonomic Veselova system
• Integrable discretization and deformation of the nonholonomic Chaplygin ball
• Discretization and superintegrability all rolled into one
• On exact discretization of the cubic-quintic Duffing oscillator
• On discretization of the Euler top
• Reducible Abelian varieties and Lax matrices for Euler's problem of two fixed centres
• Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain