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In this chapter, the (2+1)-dimensional extended perturbed nonlinear Schrödinger equation with Kerr law in the presence of spatiotemporal and chromatic dispersions is thoroughly investigated. The Schrödinger equation and its variants are crucial models in various branches of physics, particularly for their role in describing wave propagation in optical fibers, which has garnered significant attention in recent research. The primary objective of this study is to derive novel and diverse analytical solutions for this important model. To achieve this, a range of well-established and effective methods, including the Kudryashov method, generalized Kudryashov method, new Kudryashov method, modified subversion of the new extended auxiliary equation method, and Kudryashov auxiliary equation methods, have been employed. The application of these methods has led to the discovery of numerous new optical soliton solutions, encompassing a wide variety of forms such as dark, kink, singular, bright, and W-shaped solitons. Additionally, this study addresses the modulation instability of the model, identifying the conditions under which soliton solutions become unstable. The results, presented through 2D and 3D graphical representations, provide insights into the influence of equation parameters on modulation instability. No limitations were encountered during the application or interpretation of the methods. The novel optical soliton solutions, the diversity of their forms, and the comprehensive analysis of modulation instability underscore the originality and innovative contributions of this work.

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An Extensive Study on Revealing Optical Soliton Solutions and Modulation Instability of (2+1)-Dimensional Perturbed Schrödinger Equation Having Kerr Law

  • 章节

  • 发表日期：

    2025年

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  • Ismail Onder,
  • Aydin Secer,
  • Muslum Ozisik,
  • Mustafa Bayram

摘要

In this chapter, the (2+1)-dimensional extended perturbed nonlinear Schrödinger equation with Kerr law in the presence of spatiotemporal and chromatic dispersions is thoroughly investigated. The Schrödinger equation and its variants are crucial models in various branches of physics, particularly for their role in describing wave propagation in optical fibers, which has garnered significant attention in recent research. The primary objective of this study is to derive novel and diverse analytical solutions for this important model. To achieve this, a range of well-established and effective methods, including the Kudryashov method, generalized Kudryashov method, new Kudryashov method, modified subversion of the new extended auxiliary equation method, and Kudryashov auxiliary equation methods, have been employed. The application of these methods has led to the discovery of numerous new optical soliton solutions, encompassing a wide variety of forms such as dark, kink, singular, bright, and W-shaped solitons. Additionally, this study addresses the modulation instability of the model, identifying the conditions under which soliton solutions become unstable. The results, presented through 2D and 3D graphical representations, provide insights into the influence of equation parameters on modulation instability. No limitations were encountered during the application or interpretation of the methods. The novel optical soliton solutions, the diversity of their forms, and the comprehensive analysis of modulation instability underscore the originality and innovative contributions of this work.