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

We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-wave turbulence kinetic equation in the wave turbulence theory. Moreover, we construct a class of self-similar solutio...

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Detalles Bibliográficos
Autores principales: Nazarenko, Sergey, Soffer, Avy, Tran, Minh-Binh
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7515352/
http://dx.doi.org/10.3390/e21090823
Descripción
Sumario:We derive new kinetic and a porous medium equations from the nonlinear Schrödinger equation with random potentials. The kinetic equation has a very similar form compared to the four-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 with time, and this fact answers the “weak turbulence” question for the nonlinear Schrödinger equation with random potentials. We also derive Ohm’s law for the porous medium equation.

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