We study properties of chaos in generic one-dimensional nonlinear Hamiltonian
lattices comprised of weakly coupled nonlinear oscillators, by numerical
simulations of continuous-time systems and symplectic maps. For small coupling,
the measure of chaos is found to be proportional to the coupling strength and
lattice length, with the typical maximal Lyapunov exponent being proportional
to the square root of coupling. This strong chaos appears as a result of
triplet resonances between nearby modes. In addition to strong chaos we observe
a weakly chaotic component having much smaller Lyapunov exponent, the measure
of which drops approximately as a square of the coupling strength down to
smallest couplings we were able to reach. We argue that this weak chaos is
linked to the regime of fast Arnold diffusion discussed by Chirikov and
Vecheslavov. In disordered lattices of large size we find a subdiffusive
spreading of initially localized wave packets over larger and larger number of
modes. The relations between the exponent of this spreading and the exponent in
the dependence of the fast Arnold diffusion on coupling strength are analyzed.
We also trace parallels between the slow spreading of chaos and deterministic
rheology.Comment: 15 pages, 14 figure
