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<p>This paper is devoted to constructing several soliton solutions for Kudryashov’s nonlinear refractive index model, that incorporates the quadrupled-power law along with a dual form of nonlocal nonlinearity. By applying the modified simplest equation method together with Kudryashov’s method, we obtain a diverse class of optical wave patterns for the proposed problem formulated with the conformable fractional derivative. The newly derived solutions, expressed in terms of trigonometric and hyperbolic functions, can be categorized into bright, singular, dark-bright, and wave soliton types. In addition, the dynamical behavior of these newly obtained optical solutions is thoroughly examined through comprehensive graphical analyses. The influences of varying temporal parameters and different values of the fractional-order derivative are explored to highlight their roles in shaping the structural evolution of the soliton profiles. The results confirm that the analytical approaches employed namely, Kudryashov’s method and the modified simplest equation method serve as powerful and flexible tools for investigating optical solitons in nonlinear Schrödinger equations of both fractional and integer orders. Moreover, the nonlinear Schrödinger equation continues to be of significant importance in modeling the propagation of ultra-fast optical pulses in modern fiber communication systems, underscoring the practical relevance of the present study.</p>

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Soliton solutions of the Kudryashov’s law equation with dual generalized nonlocal nonlinearity via two analytical techniques

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Muhammad Amin S. Murad,
  • Ahmed H. Arnous

摘要

This paper is devoted to constructing several soliton solutions for Kudryashov’s nonlinear refractive index model, that incorporates the quadrupled-power law along with a dual form of nonlocal nonlinearity. By applying the modified simplest equation method together with Kudryashov’s method, we obtain a diverse class of optical wave patterns for the proposed problem formulated with the conformable fractional derivative. The newly derived solutions, expressed in terms of trigonometric and hyperbolic functions, can be categorized into bright, singular, dark-bright, and wave soliton types. In addition, the dynamical behavior of these newly obtained optical solutions is thoroughly examined through comprehensive graphical analyses. The influences of varying temporal parameters and different values of the fractional-order derivative are explored to highlight their roles in shaping the structural evolution of the soliton profiles. The results confirm that the analytical approaches employed namely, Kudryashov’s method and the modified simplest equation method serve as powerful and flexible tools for investigating optical solitons in nonlinear Schrödinger equations of both fractional and integer orders. Moreover, the nonlinear Schrödinger equation continues to be of significant importance in modeling the propagation of ultra-fast optical pulses in modern fiber communication systems, underscoring the practical relevance of the present study.