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<p>The objective of this paper is to investigate exact stochastic soliton solutions of a generalized nonlinear Schrödinger equation in (2+1) dimensions. This model incorporates both conformable fractional derivatives and multiplicative noise, which captures environmental randomness through the Itô calculus framework. This formulation provides a mathematical framework for examining how stochastic perturbations influence soliton dynamics in nonlinear media. The motivation stems from the need to better understand how random perturbations influence soliton dynamics in realistic physical systems, particularly in optical fibers and plasma environments where noise can strongly affect wave propagation. The improved modified extended tanh method is used as the main analytical tool. Using this approach, a broad spectrum of stochastic wave solutions is derived, including trigonometric, exponential, and Weierstrass elliptic solutions, as well as stochastic bright, dark, and singular solitons. Additionally, graphical representations illustrate how noise intensity and fractional order influence solitonic structures. These results not only deepen the theoretical understanding of fractional stochastic wave dynamics but also contribute to the theoretical analysis of fractional stochastic nonlinear wave equations and may provide insights relevant to applications in optical communication, nonlinear waveguides, and plasma physics.</p>

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Noise-driven solitons for (2+1)-dimensional conformable fractional stochastic nonlinear Schrödinger model

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Bassant Elkalzah,
  • Hamdy M. Ahmed,
  • Niveen Badra,
  • Yakup Yildirim,
  • Hatem E. Semary,
  • Islam Samir

摘要

The objective of this paper is to investigate exact stochastic soliton solutions of a generalized nonlinear Schrödinger equation in (2+1) dimensions. This model incorporates both conformable fractional derivatives and multiplicative noise, which captures environmental randomness through the Itô calculus framework. This formulation provides a mathematical framework for examining how stochastic perturbations influence soliton dynamics in nonlinear media. The motivation stems from the need to better understand how random perturbations influence soliton dynamics in realistic physical systems, particularly in optical fibers and plasma environments where noise can strongly affect wave propagation. The improved modified extended tanh method is used as the main analytical tool. Using this approach, a broad spectrum of stochastic wave solutions is derived, including trigonometric, exponential, and Weierstrass elliptic solutions, as well as stochastic bright, dark, and singular solitons. Additionally, graphical representations illustrate how noise intensity and fractional order influence solitonic structures. These results not only deepen the theoretical understanding of fractional stochastic wave dynamics but also contribute to the theoretical analysis of fractional stochastic nonlinear wave equations and may provide insights relevant to applications in optical communication, nonlinear waveguides, and plasma physics.