Journal article Open Access

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

Sergey Nazarenko, Avy Soffer, Minh-Binh Tran

### Citation Style Language JSON Export

{
"DOI": "10.3390/e21090823",
"language": "eng",
"author": [
{
"family": "Sergey Nazarenko, Avy Soffer, Minh-Binh Tran"
}
],
"issued": {
"date-parts": [
[
2019,
8,
23
]
]
},
"abstract": "<p>We derive a new kinetic and a porous medium equations from the nonlinear Schr&ouml;dinger 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 &#39;weak turbulence&#39; question for the nonlinear Schr&ouml;dinger equation with random potentials positively. We also derive Ohm&#39;s law for the porous medium equation.</p>",
"title": "On the Wave Turbulence Theory for the Nonlinear Schr\u00f6dinger Equation with Random Potentials",
"type": "article-journal",
"id": "4009820"
}
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