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>", 
  "license": "https://creativecommons.org/licenses/by/4.0/legalcode", 
  "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", 
  "image": "https://zenodo.org/static/img/logos/zenodo-gradient-round.svg", 
  "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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