关于分数薛定谔方程的周期孤子解

Fractals Pub Date : 2024-05-21 DOI:10.1142/s0218348x24400334
Rashid Ali, Devendra Kumar, A. Akgül, Ali A. Altalbe
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引用次数: 0

摘要

在这项研究中,我们使用了扩展直接代数法(EDAM)的一个新版本,即广义直接代数法(gEDAM),来研究具有保形分数导数的分数薛定谔方程(FSEs)非线性系统的周期孤子解。分数薛定谔方程是薛定谔方程的分数抽象,在量子力学中具有显著的相关性。拟议的 gEDAM 技术需要通过分数复变建立非线性常微分方程,然后求解以获得孤子解。孤子解的一些三维和轮廓图揭示了波形的周期性,为研究系统的行为提供了重要视角。这项研究通过展示众多周期性孤子解系列及其错综复杂的关系,揭示了 FSE 的动力学。这些结果不仅对理解 FSE 的动力学,而且对非线性分数偏微分方程的应用都具有重要意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
ON THE PERIODIC SOLITON SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATIONS
In this research, we use a novel version of the Extended Direct Algebraic Method (EDAM) namely generalized EDAM (gEDAM) to investigate periodic soliton solutions for nonlinear systems of fractional Schrödinger equations (FSEs) with conformable fractional derivatives. The FSEs, which is the fractional abstraction of the Schrödinger equation, grasp notable relevance in quantum mechanics. The proposed gEDAM technique entails creating nonlinear ordinary differential equations via a fractional complex transformation, which are then solved to acquire soliton solutions. Several 3D and contour graphs of the soliton solutions reveal periodicity in the wave profiles that offer crucial perspectives into the behavior of the system. The work sheds light on the dynamics of FSEs by displaying numerous families of periodic soliton solutions and their intricate relationships. These results hold significance not only for comprehending the dynamics of FSEs but also for nonlinear fractional partial differential equation applications.
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