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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{
  "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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