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<p>This paper investigates a truncated <i>M</i>-fractional (2+1)-dimensional nonlinear Schrödinger complex hyperbolic model that is used to represent different physical phenomena, including nonlinear wave propagation in optical fibers and plasma physics. We incorporate the Rational sine-Gordon expansion method to find new optical soliton solutions to the considered equation. We utilized this methodology for its effectiveness in solving nonlinear fractional partial differential equations. Using this effective method, multiple forms of soliton solutions, including bright-shape soliton, kink-type soliton, and dark soliton solutions, have been extracted from the governing equation. The resulting solutions are expressed using trigonometric and hyperbolic functions. All derived solutions are portrayed in 3D plots that showcase the physical dynamics of this model. To ensure the stability of the concerned model, we examine the modulation instability. The obtained solutions serve as guidance for the ongoing advancement of the relevant model.</p>

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Optical wave solutions of (2 + 1)-dimensional non-linear Schrödinger complex hyperbolic model with truncated M-fractional derivative by Rational sine-Gordon expansion method

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • S. Saha Ray,
  • Rajkumar Jana

摘要

This paper investigates a truncated M-fractional (2+1)-dimensional nonlinear Schrödinger complex hyperbolic model that is used to represent different physical phenomena, including nonlinear wave propagation in optical fibers and plasma physics. We incorporate the Rational sine-Gordon expansion method to find new optical soliton solutions to the considered equation. We utilized this methodology for its effectiveness in solving nonlinear fractional partial differential equations. Using this effective method, multiple forms of soliton solutions, including bright-shape soliton, kink-type soliton, and dark soliton solutions, have been extracted from the governing equation. The resulting solutions are expressed using trigonometric and hyperbolic functions. All derived solutions are portrayed in 3D plots that showcase the physical dynamics of this model. To ensure the stability of the concerned model, we examine the modulation instability. The obtained solutions serve as guidance for the ongoing advancement of the relevant model.