D.E. Pelinovsky and G. Schneider
The monoatomic FPU system as a limit of a diatomic FPU system
Applied Mathematics Letters 107 (2020), 106387 (8 pages)
Abstract:
We consider a diatomic infinite Fermi-Pasta-Ulam (FPU) system with light and
heavy particles. For a small mass ratio, we prove error estimates for the approximation of the
dynamics of this system by the dynamics of the monoatomic FPU system. The light particles are
squeezed by the heavy particles at the average value of their displacements. The error estimates
are derived by means of the energy method and hold for sufficiently long times, for which the
dynamics of the monoatomic FPU system is observed. The approximation result is restricted
to sufficiently small displacements of the heavy particles relatively to each other.
Keywords:
Fermi-Pasta-Ulam system; light and heavy particles, the small mass ratio limit, justification
of asymptotic approximations, energy estimates.