Journal article Open Access

On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials

Sergey Nazarenko, Avy Soffer, Minh-Binh Tran

We derive a new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form with the 4-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of self-similar solutions for the porous medium equation. These solutions spread infinitely as time goes to infinity and this fact answers the 'weak turbulence' question for the nonlinear Schrödinger equation with random potentials positively. We also derive Ohm's law for the porous medium equation.

Files (188.1 kB)
Name Size
1905.06323.pdf
md5:76a5e4f3436db65978f63e376ad86f92
188.1 kB Download
15
16
views
downloads
Views 15
Downloads 16
Data volume 3.0 MB
Unique views 13
Unique downloads 16

Share

Cite as