通过分岔理论求解扰动高阶非线性薛定谔方程的孤立波、周期波和扭结波

IF 5.4 2区工程技术 Q1 ENGINEERING, AEROSPACE

Propulsion and Power Research Pub Date : 2024-09-01 DOI:10.1016/j.jppr.2024.07.001

Qiancheng Ouyang , Zaiyun Zhang , Qiong Wang , Wenjing Ling , Pengcheng Zou , Xinping Li

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引用次数: 0

摘要

本文利用动力学系统的分岔理论，构建了具有五次非线性的高阶非线性薛定谔方程的行波解。首先，基于波变量，将方程转化为常微分方程。然后，在参数条件下，得到哈密顿体系和相位肖像。最后，通过沿同轴或异轴轨道积分，构建包含孤波、周期波和扭结波的行波解。此外，通过选择适当的参数值，还能以图形方式显示不同类型的解结构。此外，计算工作及其数据表明，该技术具有影响力和效率。

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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Solitary, periodic, kink wave solutions of a perturbed high-order nonlinear Schrödinger equation via bifurcation theory

In this paper, by using the bifurcation theory for dynamical system, we construct traveling wave solutions of a high-order nonlinear Schrödinger equation with a quintic nonlinearity. Firstly, based on wave variables, the equation is transformed into an ordinary differential equation. Then, under the parameter conditions, we obtain the Hamiltonian system and phase portraits. Finally, traveling wave solutions which contains solitary, periodic and kink wave solutions are constructed by integrating along the homoclinic or heteroclinic orbits. In addition, by choosing appropriate values to parameters, different types of structures of solutions can be displayed graphically. Moreover, the computational work and it's figures show that this technique is influential and efficient.

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来源期刊

Propulsion and Power Research Multiple-

CiteScore

7.50

自引率

5.70%

发文量

期刊介绍： Propulsion and Power Research is a peer reviewed scientific journal in English established in 2012. The Journals publishes high quality original research articles and general reviews in fundamental research aspects of aeronautics/astronautics propulsion and power engineering, including, but not limited to, system, fluid mechanics, heat transfer, combustion, vibration and acoustics, solid mechanics and dynamics, control and so on. The journal serves as a platform for academic exchange by experts, scholars and researchers in these fields.