The Analytical Wave Solutions for Some Class of the Nonlinea
发布时间：2023-06-19 19:52
非线性演化方程常被用来模拟现实世界中复杂的物理现象。它在物理学、生物学、光纤通信等领域有着广泛的应用。在非线性光纤中,由于超快信号路由系统和短光脉冲在通信中的广泛应用,光孤子传输成为一个非常重要的研究课题。本文对求非线性偏微分方程解析解的一些传统方法进行了改进和推广,如广义Recatti映射法、F展开法、辅助方程法和推广的修正有理展开法。我们将这些方法应用于一类非线性偏微分方程,例如修正的Kawahra方程,扰动的非线性Schrodinger方程,四阶非线性Schrodinger方程,具有二次立方非线性共振的Schrodinger方程,广义三阶Schrodinger方程和(2+1)维Heisenberg铁磁自旋链动力学模型,得到了三角、双曲、指数、有理和Jacobi椭圆函数形式的解析行波解,并运用调制稳定性分析讨论了这些模型的孤子解的性质。在给定的条件下,通过给参数赋值,给出了一些解的图形。这些图形有助于理解复杂模型的物理现象。通过给出合适的参数值,我们得到了暗孤子、亮孤子、奇异孤子、扭结孤子和反扭结孤子等新的结构。这些结构在物理学的不同分支和应用科学的其他领域有着广泛的应用。本文对一...
【文章页数】：139 页
【学位级别】：博士
【文章目录】：
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
本文编号：3835020
【文章页数】：139 页
【学位级别】：博士
【文章目录】：
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
本文编号：3835020
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