非線性演化方程常被用來模擬現(xiàn)實世界中復(fù)雜的物理現(xiàn)象。它在物理學(xué)、生物學(xué)、光纖通信等領(lǐng)域有著廣泛的應(yīng)用。在非線性光纖中,由于超快信號路由系統(tǒng)和短光脈沖在通信中的廣泛應(yīng)用,光孤子傳輸成為一個非常重要的研究課題。本文對求非線性偏微分方程解析解的一些傳統(tǒng)方法進行了改進和推廣,如廣義Recatti映射法、F展開法、輔助方程法和推廣的修正有理展開法。我們將這些方法應(yīng)用于一類非線性偏微分方程,例如修正的Kawahra方程,擾動的非線性Schrodinger方程,四階非線性Schrodinger方程,具有二次立方非線性共振的Schrodinger方程,廣義三階Schrodinger方程和(2+1)維Heisenberg鐵磁自旋鏈動力學(xué)模型,得到了三角、雙曲、指數(shù)、有理和Jacobi橢圓函數(shù)形式的解析行波解,并運用調(diào)制穩(wěn)定性分析討論了這些模型的孤子解的性質(zhì)。在給定的條件下,通過給參數(shù)賦值,給出了一些解的圖形。這些圖形有助于理解復(fù)雜模型的物理現(xiàn)象。通過給出合適的參數(shù)值,我們得到了暗孤子、亮孤子、奇異孤子、扭結(jié)孤子和反扭結(jié)孤子等新的結(jié)構(gòu)。這些結(jié)構(gòu)在物理學(xué)的不同分支和應(yīng)用科學(xué)的其他領(lǐng)域有著廣泛的應(yīng)用。本文對一...

【文章頁數(shù)】：139 頁

【學(xué)位級別】：博士

【文章目錄】：
Acknowledgements
Abstract
摘要
List of Publications
Chapter 1 Overview of the Thesis
    1.1 Introduction
    1.2 Types of solutions of NLEEs
        1.2.1 Numerical methods
        1.2.2 Qualitative methods
        1.2.3 Analytical method
    1.3 Motivation
    1.4 Objective of the study
    1.5 Justification of the study
    1.6 Organization of thesis
Chapter 2 Historical Background and Literature Review
    2.1 Nonlinear Evolution equations and its hierarchy
    2.2 The basic wave theory
        2.2.1 Traveling wave solutions
        2.2.2 The Solitary waves
        2.2.3 The Solitons
    2.3 Kinds of solitary wave and solitons
        2.3.1 Bright and dark solitons
        2.3.2 Kink and anti-kink soliton
        2.3.3 Lump soliton and rough wave
        2.3.4 Peakons solitons
        2.3.5 Compact soliton
        2.3.6 Topological solitons
        2.3.7 Envelope Solitons
        2.3.8 Gap soliton
        2.3.9 Dissipative soliton
        2.3.10 Vector solitons
        2.3.11 Vortex soliton
    2.4 Jaccobi elliptic function solutions
    2.5 Applications of solitary waves and solitons
Chapter 3 Preliminary Knowledge and Description of Methods
    3.1 Introduction
    3.2 Proposed generalized Recatti equation mapping method
    3.3 Proposed modified F-expansion method
    3.4 Proposed improved auxiliary equation method
    3.5 Proposed modified and extended Rational expansion method
    3.6 Modulation instability analysis
Chapter 4 Solitons and other Wave Solution of Modified Kawahara Equation Arising inShallow Water Waves and its Stability
    4.1 Introduction
    4.2 Solutions formation of modified Kawahara equation
        4.2.1 Gernalized Riccati equation mapping method
        4.2.2 Modified F-expansion technique
        4.2.3 Modified and extended Rational expansion method
    4.3 Stability analysis
    4.4 Discussions and physical interpretation of results
    4.5 Conclusion
Chapter 5 Optical Solitons and Eliptic Function Solutions of Perturbed NLSE with PowerLaw Nonlinearity in Non-Kerr Medium and its Modulation Instability
    5.1 Introduction
    5.2 Governing model
    5.3 Solitons formation of Perturbed NLSE with power law nonlinearity in non-ker medium
        5.3.1 The proposed improved auxiliary equation method
        5.3.2 The proposed gernalized Riccatti equation mapping method
    5.4 Modulation instability
    5.5 Results discussion and physical explanation of solutions
    5.6 Conclusion
Chapter 6 Structure of Optical Solitons of Resonant and Generalized Third-Order Nonlin-ear Schrodinger Equations and their Modulation Instability Analysis
    6.1 Introduction
    6.2 Solitons of resonant NLSE with quadratic-cubic nonlinearity
    6.3 Soliton formation of generalized third-order NLSE
    6.4 Modulation instability analysis
        6.4.1 Resonant NLSE with quadratic-cubic non-linearity
        6.4.2 Generalized third-order NLSE
    6.5 Results interpretation physically and discussions
    6.6 Conclusion
Chapter 7 Arising Wave propagation in Nonlinear Media for the(2+1)-dimensional Heisen-berg Ferromagnetic Spin Chain Dynamical Model and its Stability
    7.1 Introduction
    7.2 Application of proposed methods on (2+1)-dimensional Heisenberg Ferro-magnetic Spin Chain dynamical model
        7.2.1 Soliton solution of HFSC by auxiliary method
        7.2.2 Soliton solution of HFSC By Riccati mapping method
    7.3 Modulation instability analysis
    7.4 Results and discussion
    7.5 Concluding remarks
Chapter 8 Conclusions
    8.1 Summary of the research
    8.2 Future research
Bibliography



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