光纤中出现的分数薛定谔方程的新视角

Fractals Pub Date : 2024-02-20 DOI:10.1142/s0218348x24500348
KANG-LE WANG
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引用次数: 0

摘要

本文用贝塔导数描述了分数薛定谔方程,并用它来阐明超短脉冲与光纤中量子特性的动态相互作用。本研究采用分数库德里亚肖夫法、分数余弦正弦法和分数 tanh 函数法等三种强大而简单的数学方法,研究分数薛定谔方程的孤波和周期解。研究结果表明,所提出的三种计算方法简单、高效、简洁,可用于研究更复杂的现象。最后,通过绘制一些具有适当参数的三维图形,说明了所获得的孤波解的动力学行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
NOVEL PERSPECTIVE TO THE FRACTIONAL SCHRÖDINGER EQUATION ARISING IN OPTICAL FIBERS

In this paper, the fractional Schrödinger equation is described with beta derivative, which is used to elucidate the dynamic interaction of ultra-short pulses with quantum properties in optical fibers. This work is to study the solitary wave and periodic solutions of the fractional Schrödinger equation by employing three powerful and simple mathematical approaches like fractional Kudryashov method, fractional cosine–sine method and fractional tanh function method. The acquired outcomes illustrate that the proposed three computational approaches are simple, efficient, concise and can be adopted to study more complex phenomena. Finally, the dynamical behavior of these acquired solitary wave solutions is illustrated by sketching some 3D figures with proper parameters.

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