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<p>The stability analysis of evolutionary and nonlinear dynamical systems is essential for understanding their robustness and long-term behavior. Stability can be examined in three key approaches, stability of an initial state (initial value problem), stability of a steady-state, and stability of a traveling wave solution. Two main approaches exist, linear and nonlinear stability analysis. Notably, the stability of steady states has received limited attention in the literature. The initial value problem is typically addressed through the linear perturbation of a specific solution, leading to an eigenvalue equation, and by solving the resulting boundary value problem by imposing appropriate conditions on eigenfunctions. However, there is no universally recognized method for solving this problem. Prior attempts, such as the application of the energy integral criteria in Seadawy et&#xa0;al. (<CitationRef CitationID="CR2">2023</CitationRef>), have been found to be incorrect.</p>

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Comments on the paper: applications for mixed Chen–Lee–Liu derivative nonlinear Schrodinger equation in water wave flumes and optical fibers. Opt. Quant. Electron 55, 34 (2023)

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    2025年3月20日

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  • H. I. Abdel-Gawad

摘要

The stability analysis of evolutionary and nonlinear dynamical systems is essential for understanding their robustness and long-term behavior. Stability can be examined in three key approaches, stability of an initial state (initial value problem), stability of a steady-state, and stability of a traveling wave solution. Two main approaches exist, linear and nonlinear stability analysis. Notably, the stability of steady states has received limited attention in the literature. The initial value problem is typically addressed through the linear perturbation of a specific solution, leading to an eigenvalue equation, and by solving the resulting boundary value problem by imposing appropriate conditions on eigenfunctions. However, there is no universally recognized method for solving this problem. Prior attempts, such as the application of the energy integral criteria in Seadawy et al. (2023), have been found to be incorrect.