Journal article Open Access

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

Sergey Nazarenko, Avy Soffer, Minh-Binh Tran

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{
"inLanguage": {
"alternateName": "eng",
"@type": "Language",
"name": "English"
},
"description": "<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>",
"creator": [
{
"@type": "Person",
"name": "Sergey Nazarenko, Avy Soffer, Minh-Binh Tran"
}
],
"headline": "On the Wave Turbulence Theory for the Nonlinear Schr\u00f6dinger Equation with Random Potentials",
"datePublished": "2019-08-23",
"url": "https://zenodo.org/record/4009820",
"keywords": [
"wave turbulence theory; nonlinear schr\u00f6dinger equation with random potentials; 4-wave kinetic turbulence equation; ohm's law; porous medium equation."
],
"@context": "https://schema.org/",
"identifier": "https://doi.org/10.3390/e21090823",
"@id": "https://doi.org/10.3390/e21090823",
"@type": "ScholarlyArticle",
"name": "On the Wave Turbulence Theory for the Nonlinear Schr\u00f6dinger Equation with Random Potentials"
}
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