  We propose a model for a chain of particles coupled by nonlinear springs in
which each mass has an internal mass and all interactions are assumed to be
nonlinear. We show how to construct an asymptotic solution of this system using
multiple timescales, the systematic solution of coupled equations by repeated
application of a consistency condition. Our results show that for some
combinations of nonlinearity the dynamics are governed by the NLS as in the
more usual mass-in-mass chains with linear interactions between inner and outer
masses. However, when both nonlinearities have quadratic components, we show
that the asymptotic reduction results in a Ginzburg-Landau equation instead of
NLS.
