  We propose a model for a chain vibrating in 3 dimensions (3D), with first
neighbors anharmonic interatomic potential which depends on their distance, and
subjected to an external tension.
  In the framework of the non-linear fluctuating hydrodynamic theory (NLFHT),
that was successfully applied to 1D chains, we obtain a heat mode, two
longitudinal and four transverse sound modes. We compute their spatio-temporal
correlations comparing the theoretical results with molecular dynamics
simulations, finding a good agreement for high temperatures. We find that the
transverse sound modes behave diffusively, meanwhile the heat and longitudinal
sound modes superdiffusively, exploring their possible scaling functions and
characteristic exponents.
