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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  <identifier identifierType="URL">https://zenodo.org/record/4009820</identifier>
  <creators>
    <creator>
      <creatorName>Sergey Nazarenko, Avy Soffer, Minh-Binh Tran</creatorName>
    </creator>
  </creators>
  <titles>
    <title>On the Wave Turbulence Theory for the Nonlinear Schrödinger Equation with Random Potentials</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2019</publicationYear>
  <subjects>
    <subject>wave turbulence theory; nonlinear schrödinger equation with random potentials; 4-wave kinetic turbulence equation; ohm's law; porous medium equation.</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2019-08-23</date>
  </dates>
  <language>en</language>
  <resourceType resourceTypeGeneral="JournalArticle"/>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/4009820</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsIdenticalTo">10.3390/e21090823</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;We derive a new kinetic and a porous medium equations from the nonlinear Schr&amp;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 &amp;#39;weak turbulence&amp;#39; question for the nonlinear Schr&amp;ouml;dinger equation with random potentials positively. We also derive Ohm&amp;#39;s law for the porous medium equation.&lt;/p&gt;</description>
  </descriptions>
  <fundingReferences>
    <fundingReference>
      <funderName>European Commission</funderName>
      <funderIdentifier funderIdentifierType="Crossref Funder ID">10.13039/501100000780</funderIdentifier>
      <awardNumber awardURI="info:eu-repo/grantAgreement/EC/H2020/823937/">823937</awardNumber>
      <awardTitle>Hydrodynamical approach to light turbulence</awardTitle>
    </fundingReference>
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