分数阶非线性Schrödinger方程小振幅单向波的分岔分析。

IF 3.9 2区综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES

Scientific Reports Pub Date : 2025-03-22 DOI:10.1038/s41598-025-94391-6

Safoura Rezaei Aderyani, Reza Saadati, Mohammad Saeid Abolhassanifar, Donal O'Regan

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引用次数: 0

摘要

本研究探讨非线性时相关Schrödinger方程及相关模型的分岔现象，应用Kudryashov方法求精确解。将分析扩展到分数阶动力学的非线性时间分数阶Schrödinger方程和带beta导数的时空修正Benjamin-Bona-Mahony方程。本文导出了解析解，重点讨论了分数阶导数对波传播的影响。分岔分析显示了参数变化如何影响系统行为，用波解的可视化表示说明了参数对波稳定性和形态的影响。这项工作提高了对分数阶微分方程在流体动力学、非线性光学和量子力学等领域的理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bifurcation analysis of small amplitude unidirectional waves for nonlinear Schrödinger equations with fractional derivatives.

This study explores bifurcation phenomena in the nonlinear time-dependent Schrödinger equation and related models, applying Kudryashov's methods to find exact solutions. It extends the analysis to the nonlinear time fractional Schrödinger equation and the space-time modified Benjamin-Bona-Mahony equation with beta derivatives for fractional dynamics. The paper derives analytical solutions, highlighting the impact of fractional derivatives on wave propagation. A bifurcation analysis shows how parameter changes affect system behavior, with visual representations of wave solutions illustrating the influence of parameters on wave stability and morphology. The work enhances the understanding of fractional differential equations in fields like fluid dynamics, nonlinear optics, and quantum mechanics.

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来源期刊

Scientific Reports Natural Science Disciplines-

CiteScore

7.50

自引率

4.30%

发文量

19567

审稿时长

3.9 months

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