Mathematical Methods and Traveling Wave Solutions of the Non

发布时间：2021-04-02 07:57

　　本文分析了三维非线性孤波在磁化的正电子等离子体中的传播。这些非线性孤立波以模型的形式进行研究。应用新的技巧对源自于不同应用领域的非线性模型精确行波解进行了研究。对“修正扩展映射法”进行了进一步修正并应用于不同的非线性偏微分方程。这些新技巧成功地研究了源自于磁化正电子等离子体非线性物理模型中的偏微分方程。利用数学软件Mathematica,得到了周期波、扭结与反扭结、暗孤子与亮孤子、亮孤子与暗孤子波等不同类型的孤立波解。这些孤波解表示电场势。电场、磁场和量子统计压力由电场势导出。所有结果均以双曲函数、三角函数和有理函数的形式表示。分析了孤立波解的孤子稳定性,并对部分解的稳定性进行了验证。给出了电场势、电场和磁场的图示。这些结果与其他研究者使用不同方法得到的解进行了比较。计算结果表明,该方法具有较高的计算效率和计算精度,可应用于其它源自于等离子体物理、数学物理、工程、流体力学等应用科学中的数学物理问题。这些解在物理学的不同分支和工程的其他领域都很重要,为研究人员研究和理解系统的物理解释提供帮助。 

【文章来源】：江苏大学江苏省

【文章页数】：75 页

【学位级别】：硕士

【文章目录】：
Acknowledgements
Abstract
摘要
List of Publications
1 Introduction
    1.1 Background
    1.2 Literature Review
        1.2.1 Plasma Modeling
        1.2.2 Traveling Wave Solutions
    1.3 Problem Statement
    1.4 Organization
2 Preliminaries
    2.1 Overview
    2.2 Plasma
        2.2.1 Applications of Plasma
    2.3 Mathematical Modeling
        2.3.1 Linear Model
        2.3.2 Nonlinear Model
    2.4 Plasma Modeling
    2.5 Traveling Wave
    2.6 Solitary wave
    2.7 Soliton
    2.8 Stability analysis
        2.8.1 Stability
        2.8.2 Soliton Stability
    2.9 Electric and Magnetic Fields
3 Mathematical Methods and Traveling Wave Solutions of Nonlinear Physical Mod-els
    3.1 Modified Extended Mapping Method
    3.2 Application of the Method to Three DimensionalZakharov-Kuznetsov-Burgers Equation
        3.2.1 Zakharov-Kuznetsov-Burgers Equation
        3.2.2 Solitary Wave Solutions of Zakharov-Kuznetsov-Burgers Equation ina Magnetized Electron-Positron Plasma and Their Application
    3.3 Application of the Method to Hirota equation
4 Stability Analysis of the Traveling Wave Solutions
    4.1 Three-dimensional Nonlinear Modified Zakharov-Kuznetsov Equation
    4.2 Traveling Wave Solutions of the Three-dimensional Nonlinear Modified Zakharov-Kuznetsov Equation and Their Stability Analysis
5 Results and Discussion
    5.1 Relationship to Previous Research
    5.2 Conclusion
Bibliography


【参考文献】：
期刊论文
[1]New Exact Travelling Wave Solutions to Hirota Equation and （1+1）-Dimensional Dispersive Long Wave Equation[J]. WANG Qi~(1,4) CHEN Yong~(2,3,4) LI Biao~(1,4) ZHANG Hong-Qing~(1,4)~1Department of Applied Mathematics,Dalian University of Technology,Dalian 116024,China~2Department of Physics,Ningbo University,Ningbo 315211,China ~3Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China ~4Key Laboratory of Mathematics and Mechanization,the Chinese Academy of Sciences,Beijing 100080,China.  Communications in Theoretical Physics. 2004(06)



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