<p>In this paper, the new extended direct mapping technique is utilized to investigate the present nonlinear Schrödinger equation with conformable derivative, leading to the construction of different new optical soliton solutions. The constructed optical solutions, including bright soliton, dark soliton, W-shaped soliton, and wave soliton solutions, are successfully derived. To illustrate the dynamical behavior of the present soliton solutions, various plots of the form of two-dimensional and three-dimensional, and contour plots are visualized through graphical simulations. Further, the impact of the different parameters, namely, the temporal parameter and conformable derivative parameter on the results is discussed, highlighting their important roles in shaping soliton characteristics. A main contribution of this study lies in examining fractional-order and temporal dynamics and their influence on soliton behavior, which allow for better control and optimization of soliton characteristics. This work strengthens the theoretical understanding of the nonlinear Schrödinger equation and provides a solid foundation for practical applications, including wave propagation in nonlinear optical fibers.</p>

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Formulation and dynamical behavior of soliton solutions to the nonlinear Schrödinger equation with Kudryashov’s generalized nonlinear refractive index

  • Muhammad Amin S. Murad

摘要

In this paper, the new extended direct mapping technique is utilized to investigate the present nonlinear Schrödinger equation with conformable derivative, leading to the construction of different new optical soliton solutions. The constructed optical solutions, including bright soliton, dark soliton, W-shaped soliton, and wave soliton solutions, are successfully derived. To illustrate the dynamical behavior of the present soliton solutions, various plots of the form of two-dimensional and three-dimensional, and contour plots are visualized through graphical simulations. Further, the impact of the different parameters, namely, the temporal parameter and conformable derivative parameter on the results is discussed, highlighting their important roles in shaping soliton characteristics. A main contribution of this study lies in examining fractional-order and temporal dynamics and their influence on soliton behavior, which allow for better control and optimization of soliton characteristics. This work strengthens the theoretical understanding of the nonlinear Schrödinger equation and provides a solid foundation for practical applications, including wave propagation in nonlinear optical fibers.