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<p>Under investigation is a reverse time nonlocal generalized nonlinear Schrödinger equation, which can be derived from a special reduction of the coupled generalized nonlinear Schrödinger equations with four-wave mixing effect. The <i>N</i>-fold Darboux transformation related to a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11129_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\times 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> matrix spectral problem with two symmetry relationships has been constructed. As an application, the <i>N</i>-soliton solution under zero background as well as the <i>N</i>-breather and <i>N</i>th-order rogue wave solutions under nonzero background have been obtained. The dynamic behaviors of bright one- and two-solitons are demonstrated. The Kuznetsov–Ma breather, Akhmediev breather, the fission, fusion and crossing of breathers, and the hybrid types of breathers are presented. Furthermore, first- and second-order rogue waves and the interactions between rogue waves and breathers are discussed through graphical simulations.</p>

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Solitons, breathers and rogue waves in a reverse time nonlocal generalized nonlinear Schrödinger equation with four-wave mixing effect

  • 期刊论文

  • 发表日期：

    2025年4月14日

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  • Junyan Wang,
  • Yihao Li,
  • Jiao Wei

摘要

Under investigation is a reverse time nonlocal generalized nonlinear Schrödinger equation, which can be derived from a special reduction of the coupled generalized nonlinear Schrödinger equations with four-wave mixing effect. The N-fold Darboux transformation related to a \(3\times 3\) 3 × 3 matrix spectral problem with two symmetry relationships has been constructed. As an application, the N-soliton solution under zero background as well as the N-breather and Nth-order rogue wave solutions under nonzero background have been obtained. The dynamic behaviors of bright one- and two-solitons are demonstrated. The Kuznetsov–Ma breather, Akhmediev breather, the fission, fusion and crossing of breathers, and the hybrid types of breathers are presented. Furthermore, first- and second-order rogue waves and the interactions between rogue waves and breathers are discussed through graphical simulations.