On the Wave Turbulence Theory for the Nonlinear Schr\"odinger Equation with Random Potentials
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Publication:6318823
arXiv1905.06323MaRDI QIDQ6318823
Sergey V. Nazarenko, Avy Soffer, Minh-Binh Tran
Publication date: 14 May 2019
Abstract: We derive a new kinetic and a porous medium equations from the nonlinear Schr"odinger 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 Schr"odinger equation with random potentials positively. We also derive Ohm's law for the porous medium equation.
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