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<p>We consider nonlinear dispersive equations of Schrödinger-type involving fractional powers <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="332_2025_10145_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="71" /> </InlineMediaObject> <EquationSource Format="TEX">\(0&lt;s\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>s</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical <i>s</i> and provide evidence for a novel type of highly oscillatory singularity within the solution.</p>

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Numerical Evidence for Singularity Formation in Defocusing Fractional NLS in One Space Dimension

  • 期刊论文

  • 发表日期：

    2025年3月6日

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  • Christian Klein,
  • Christof Sparber

摘要

We consider nonlinear dispersive equations of Schrödinger-type involving fractional powers \(0<s\le 1\) 0 < s ≤ 1 of the Laplacian and a defocusing power-law nonlinearity. We conduct numerical simulations in the case of small, energy supercritical s and provide evidence for a novel type of highly oscillatory singularity within the solution.