Energy spreading in strongly nonlinear disordered lattices. (English) Zbl 1451.34039
Summary: We study the scaling properties of energy spreading in disordered strongly nonlinear Hamiltonian lattices. Such lattices consist of nonlinearly coupled local linear or nonlinear oscillators, and demonstrate a rather slow, subdiffusive spreading of initially localized wave packets. We use a fractional nonlinear diffusion equation as a heuristic model of this process, and confirm that the scaling predictions resulting from a self-similar solution of this equation are indeed applicable to all studied cases. We show that the spreading in nonlinearly coupled linear oscillators slows down compared to a pure power law, while for nonlinear local oscillators a power law is valid in the whole studied range of parameters.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 35C06 | Self-similar solutions to PDEs |
Software:
odeintReferences:
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