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<p>This study, investigates the optical soliton solutions of the (2+1)-dimensional Biswas–Milovic equation in the presence of perturbation effects together with parabolic and Kerr laws of self-phase modulation. The new Kudryashov method is employed to construct a wide class of exact analytical solutions in closed form. The obtained solutions are systematically verified through contour, two-dimensional, and three-dimensional graphical representations under suitable parameter constraints, ensuring their physical consistency and validity. Various nonlinear wave structures, including bright, dark, and degenerate dark solitons, which are essential in describing nonlinear optical propagation phenomena, are successfully derived. Furthermore, the modulation instability characteristics of the considered model are analyzed to examine the stability behavior of the obtained wave solutions. The results demonstrate the effectiveness of the proposed analytical approach and highlight its capability to generate physically meaningful solutions for higher-dimensional nonlinear models. Overall, the findings provide valuable insights into the mathematical structure of the Biswas–Milovic equation and may stimulate further research on multidimensional nonlinear wave systems in optical physics.</p>

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The (2+1)-dimensional perturbed Biswas-Milovic equation having the Kerr and parabolic laws: revealing the optical solitons and modulation instability analysis

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Hasan Cakicioglu,
  • Muslum Ozisik,
  • Aydin Secer,
  • Karim K. Ahmed

摘要

This study, investigates the optical soliton solutions of the (2+1)-dimensional Biswas–Milovic equation in the presence of perturbation effects together with parabolic and Kerr laws of self-phase modulation. The new Kudryashov method is employed to construct a wide class of exact analytical solutions in closed form. The obtained solutions are systematically verified through contour, two-dimensional, and three-dimensional graphical representations under suitable parameter constraints, ensuring their physical consistency and validity. Various nonlinear wave structures, including bright, dark, and degenerate dark solitons, which are essential in describing nonlinear optical propagation phenomena, are successfully derived. Furthermore, the modulation instability characteristics of the considered model are analyzed to examine the stability behavior of the obtained wave solutions. The results demonstrate the effectiveness of the proposed analytical approach and highlight its capability to generate physically meaningful solutions for higher-dimensional nonlinear models. Overall, the findings provide valuable insights into the mathematical structure of the Biswas–Milovic equation and may stimulate further research on multidimensional nonlinear wave systems in optical physics.