On exact discretization of the cubic-quintic Duffing oscillator

Abstract

Application of intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few exact discretizations of one-dimensional cubic and quintic Duffing oscillators sharing form of Hamiltonian and canonical Poisson bracket up to the integer scaling factor.

16 pages, 3 figures, LaTex with AMS fonts

References in corpus (5)

• Simultaneous separation for the Neumann and Chaplygin 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

Cited by in corpus (2)

• Elliptic curve arithmetic and superintegrable systems
• Discretization and superintegrability all rolled into one