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<p>The optical soliton solutions for the fractional-order nonlinear Schrödinger equation with parabolic law are investigated in the present study. The analysis employs conformable fractional derivatives, beta derivatives, and truncated <i>M</i>-fractional derivatives to analyze the impact of fractional derivatives on the behavior of NLSE solitons. First, we used a transformation that converts the proposed partial differential equation into a nonlinear ordinary differential equation. We extract novel exact traveling wave solutions, including hyperbolic trigonometric, trigonometric, exponential, and rational functions, using the generalized auxiliary equation method and the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2148_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <msup> <mi>G</mi> <mo>′</mo> </msup> </mfrac> <mo>)</mo> </mrow> </math></EquationSource> <EquationSource Format="TEX">$\left (\frac{1}{G'}\right )$</EquationSource> </InlineEquation>-expansion method. The results reveal a variety of soliton solutions, such as kink, anti-kink, bright, dark, and periodic presenting the versatility of the proposed methods in generating solutions with distinct physical behaviors. Graphical representations of the solutions in both 2-D and 3-D provide a deeper understanding of the influence of fractional derivatives on soliton propagation. This work contributes to the field of wave propagation in optical fibers.</p>

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Investigation of optical soliton solutions for the fractional-order nonlinear Schrödinger equation including parabolic law of nonlinearity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月30日

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  • Shah Muhammad,
  • Abdul Saboor,
  • Muhammad Shakeel,
  • Hameed Gul Ahmadzai

摘要

The optical soliton solutions for the fractional-order nonlinear Schrödinger equation with parabolic law are investigated in the present study. The analysis employs conformable fractional derivatives, beta derivatives, and truncated M-fractional derivatives to analyze the impact of fractional derivatives on the behavior of NLSE solitons. First, we used a transformation that converts the proposed partial differential equation into a nonlinear ordinary differential equation. We extract novel exact traveling wave solutions, including hyperbolic trigonometric, trigonometric, exponential, and rational functions, using the generalized auxiliary equation method and the ( 1 G ′ ) $\left (\frac{1}{G'}\right )$ -expansion method. The results reveal a variety of soliton solutions, such as kink, anti-kink, bright, dark, and periodic presenting the versatility of the proposed methods in generating solutions with distinct physical behaviors. Graphical representations of the solutions in both 2-D and 3-D provide a deeper understanding of the influence of fractional derivatives on soliton propagation. This work contributes to the field of wave propagation in optical fibers.