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<p>In this article, we propose a time-splitting multidomain Fourier-Chebyshev spectral method to compute rogue wave solutions to the two-dimensional nonlinear Schrödinger equation in the whole space, which usually decay very slowly at the far field. To approximate the slow-decay function over the whole space, we first expand the wave function with Fourier basis in the azimuthal direction, then propose the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10915_2025_3070_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation>-continuity multidomain Chebyshev spectral method in the radial direction. Our scheme is second order in time and spectrally accurate in space. Extensive numerical results, together with theoretical analysis, are presented to confirm the efficiency and accuracy for wave functions with different decay rates. In addition, the successful simulation of rogue wave further validates our method.</p>

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Multidomain Fourier-Chebyshev Spectral Method for Computing Rogue waves in the Nonlinear Schrödinger Equation

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Sheng Chen,
  • Guangshen Liu,
  • Zhiguo Xu,
  • Yong Zhang

摘要

In this article, we propose a time-splitting multidomain Fourier-Chebyshev spectral method to compute rogue wave solutions to the two-dimensional nonlinear Schrödinger equation in the whole space, which usually decay very slowly at the far field. To approximate the slow-decay function over the whole space, we first expand the wave function with Fourier basis in the azimuthal direction, then propose the \(C^1\) C 1 -continuity multidomain Chebyshev spectral method in the radial direction. Our scheme is second order in time and spectrally accurate in space. Extensive numerical results, together with theoretical analysis, are presented to confirm the efficiency and accuracy for wave functions with different decay rates. In addition, the successful simulation of rogue wave further validates our method.