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We consider a nonlinear chain of coupled oscillators, which is a directgeneralization of the classical FPU lattice and exhibits, besides the usualnearest neighbor interaction, also next-to-nearest neighbor interaction. Forthe case of nearest neighbor attraction and next-to-nearest neighbor repulsionwe prove that such a lattice admits, in contrast to the classical FPU model,moving modulating front solutions of permanent form, which have smallconverging tails at infinity and can be approximated by solitary wave solutionsof the Nonlinear Schr\"odinger equation. When the associated potentials areeven, then the proof yields moving modulating pulse solutions of permanentform, whose profiles are spatially localized. Our analysis employs the spatialdynamics approach as developed by Iooss and Kirchg\"assner. The relevantsolutions are constructed on a five-dimensional center manifold and theirpersistence is guaranteed by reversibility arguments.

Moving modulating pulse and front solutions of permanent form in a FPU model with nearest and next-to-nearest neighbor interaction