  We consider a nonlinear chain of coupled oscillators, which is a direct
generalization of the classical FPU lattice and exhibits, besides the usual
nearest neighbor interaction, also next-to-nearest neighbor interaction. For
the case of nearest neighbor attraction and next-to-nearest neighbor repulsion
we prove that such a lattice admits, in contrast to the classical FPU model,
moving modulating front solutions of permanent form, which have small
converging tails at infinity and can be approximated by solitary wave solutions
of the Nonlinear Schr\"odinger equation. When the associated potentials are
even, then the proof yields moving modulating pulse solutions of permanent
form, whose profiles are spatially localized. Our analysis employs the spatial
dynamics approach as developed by Iooss and Kirchg\"assner. The relevant
solutions are constructed on a five-dimensional center manifold and their
persistence is guaranteed by reversibility arguments.
