本文分析了三維非線性孤波在磁化的正電子等離子體中的傳播。這些非線性孤立波以模型的形式進(jìn)行研究。應(yīng)用新的技巧對(duì)源自于不同應(yīng)用領(lǐng)域的非線性模型精確行波解進(jìn)行了研究。對(duì)“修正擴(kuò)展映射法”進(jìn)行了進(jìn)一步修正并應(yīng)用于不同的非線性偏微分方程。這些新技巧成功地研究了源自于磁化正電子等離子體非線性物理模型中的偏微分方程。利用數(shù)學(xué)軟件Mathematica,得到了周期波、扭結(jié)與反扭結(jié)、暗孤子與亮孤子、亮孤子與暗孤子波等不同類型的孤立波解。這些孤波解表示電場(chǎng)勢(shì)。電場(chǎng)、磁場(chǎng)和量子統(tǒng)計(jì)壓力由電場(chǎng)勢(shì)導(dǎo)出。所有結(jié)果均以雙曲函數(shù)、三角函數(shù)和有理函數(shù)的形式表示。分析了孤立波解的孤子穩(wěn)定性,并對(duì)部分解的穩(wěn)定性進(jìn)行了驗(yàn)證。給出了電場(chǎng)勢(shì)、電場(chǎng)和磁場(chǎng)的圖示。這些結(jié)果與其他研究者使用不同方法得到的解進(jìn)行了比較。計(jì)算結(jié)果表明,該方法具有較高的計(jì)算效率和計(jì)算精度,可應(yīng)用于其它源自于等離子體物理、數(shù)學(xué)物理、工程、流體力學(xué)等應(yīng)用科學(xué)中的數(shù)學(xué)物理問(wèn)題。這些解在物理學(xué)的不同分支和工程的其他領(lǐng)域都很重要,為研究人員研究和理解系統(tǒng)的物理解釋提供幫助。 

【文章來(lái)源】：江蘇大學(xué)江蘇省

【文章頁(yè)數(shù)】：75 頁(yè)

【學(xué)位級(jí)別】：碩士

【文章目錄】：
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


【參考文獻(xiàn)】：
期刊論文
[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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