The study of nonlinear elastodynamics systems it's very dificult because of the complexity of the nonlinear partial differential equations, in many cases result much more convenient try to understand the statistical properties of the system.

According to the theory of weak turbulence (successfully applied in the past to plasma, optics, and hydrodynamic waves), a nonlinear wave system evolves at long times with a slow transfer of energy from one mode to another and it's possible to derive a kinetic equation for the spectral transfer in terms of the second order moment.

Our aim is to describe the long-time evolution of waves in elastic media and find how is the transport of the conserved quantities.

People involved

Sergio Rica (LPS-ENS, CNRS / Universidad de Chile)
Gustavo Düring (Universidad de Chile)

References

[1] D.J. Benney, P.G. Saffman, Proc. Roy. Soc. London A 289, 301 (1966).
[2] V. E. Zakharov, V. S. L'vov and G. Falkovich, Kolmogorov Spectra of Turbulence I (Springer,Berlin, 1992).
[3] A. Newell, S. Nazarenko, L. Biven, Physica D 152 - 153 520 (2001).
[4] S. Dyachenko et al., Physica D 57, 96 (1992).