Journal article Open Access

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

Sergey Nazarenko, Avy Soffer, Minh-Binh Tran

### DataCite XML Export

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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="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>
</fundingReferences>
</resource>

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