  We study the relaxation dynamics of a coarse-grained polymer chain at
different degrees of stretching by both analytical means and numerical
simulations. The macromolecule is modelled as a string of beads, connected by
anharmonic springs, subject to a tensile force applied at the end monomer of
the chain while the other end is fixed at the origin of coordinates. The impact
of bond non-linearity on the relaxation dynamics of the polymer at different
degrees of stretching is treated analytically within the Gaussian
self-consistent approach (GSC) and then compared to simulation results derived
from two different methods: Monte-Carlo (MC) and Molecular Dynamics (MD).
  At low and medium degrees of chain elongation we find good agreement between
GSC predictions and the Monte-Carlo simulations. However, for strongly
stretched chains the MD method, which takes into account inertial effects,
reveals two important aspects of the nonlinear interaction between monomers:
(i) a coupling and energy transfer between the damped, oscillatory normal modes
of the chain, and (ii) the appearance of non-vanishing contributions of a
continuum of frequencies around the characteristic modes in the power spectrum
of the normal mode correlation functions.
