Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions

We study the dynamics of Fermi-Pasta-Ulam (FPU) chains with both harmonic and anharmonic power-law long-range interactions. We show that the dynamics is described in the continuum limit by a Generalized Fractional Boussinesq differential Equation (GFBE), whose derivation is performed in full detail. We also discuss a version of the model where couplings are alternating in sign.