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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    <subfield code="a">&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;</subfield>
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    <subfield code="a">wave turbulence theory; nonlinear schrödinger equation with random potentials; 4-wave kinetic turbulence equation; ohm's law; porous medium equation.</subfield>
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