This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate the dynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.
Author(s): Emmanuel Kengne, WuMing Liu
Publisher: Springer
Year: 2023
Language: English
Pages: 524
City: Singapore
Preface
Acknowledgements
Contents
About the Authors
Abbreviations and Acronyms
Part I Engineering Nonlinear Modulated Waves in Nonlinear Transmission Networks
1 Introduction
References
2 Nonlinear Schrödinger Models for Solitons Propagation in 1D Lossless Nonlinear Transmission Networks (NLTNs)
2.1 Introduction
2.2 Standard Nonlinear Schrödinger Equations for Modulated Waves Propagation in a Lossless Electrical Transmission the Network: Effects of the Dispersive Element CS
2.2.1 Model Equations
2.2.2 Bright and Dark Single-Solitary Waves Propagating in the 1D Lossless Network of Fig. 2.1
2.3 Modulational Instability and Transmission of Chirped Femtosecond Signals Through the Lossless Electrical Network of Fig. 2.1
2.3.1 Introduction
2.3.2 Modulational Instability and Evolution of Chirped Femtosecond Solitary Signals Embedded on a Non-vanishing CW Background
2.3.3 Sister Femtosecond Nonlinear Modulated Waves with Two Nonlinear Chirp Terms
References
3 Transmission of Dissipative Solitonlike Signals Through One-Dimensional Transmission Networks
3.1 Chirped Lambert W-Kink Waves Propagation in a Lossy Electrical …
3.1.1 Introduction
3.1.2 Amplitude Equation
3.1.3 Baseband Modulational Instability Analysis
3.1.4 Evolution of Chirped Lambert W-Kink Pulses in the Network of Fig. 2.1
3.2 Spatiotemporal Modulation of Damped Solitonlike Wave …
3.2.1 Introduction
3.2.2 Linear Dispersion Relation and Spatial Decreasing Rate
3.2.3 Amplitude Equation and Modulated Damped
3.2.4 Linear Stability
3.2.5 Spatiotemporal Modulated Signals Propagating Through the Network of Fig. 3.8
3.2.6 Transmission of Spatiotemporal Modulated Damped Envelope Signals Through a Lossy Network
3.3 Modulated Wavetrains in a Dissipative Bi-Inductance Transmission Network
3.3.1 Introduction and Circuit Equations
3.3.2 Generalized Cubic-Quintic Complex Ginzburg-Landau Equation for a Lossy Network
3.3.3 Linear Analysis and Modulational Instability
3.3.4 Coherent Structures
References
4 Emission of Rogue Wave Signals in Nonlinear Electrical Transmission Networks
4.1 Emission of Rogue Wave Signals Through the Modified …
4.1.1 Introduction
4.1.2 Modulated Waves and Linear Analysis
4.1.3 Construction of Rogue Waves in the Lossless Network Under the Condition PQ>0
4.1.4 Emission of Rogue Wave Signals Through the Network of Fig. 2.1摥映數爠eflinkfig2.12.12
4.1.5 Conclusion and Discussions
4.2 Generation of Network Modulated Rogue Waves Under …
4.2.1 The Kundu–Eckhaus Model for Non-autonomous Modulated Rogue Waves in a Lossless Electric Network
4.2.2 Generation of First-Order Non-autonomous Modulated Rogue Waves (Alias Peregrine Solitons) for a Lossless Electric Network
4.2.3 Conclusion and Discussions
4.3 Chirped Super Rogue Waves Propagating …
4.3.1 Generalized Nonlinear Schrödinger Equation for a Lossless Electric Network
4.3.2 Phase Engineering Chirped Super Rogue Waves for a Lossless Electric Network
4.3.3 Computational/Numerical Simulations
4.3.4 Conclusion and Discussion
References
5 Emission of Nonlinear Modulated Waves in Multi-coupled Nonlinear Transmission Networks
5.1 Transmission of Solitonlike Wave Signals in a Two-Dimensional Lossless Dispersive Nonlinear Transmission Network
5.1.1 Description of the and Network Equations
5.1.2 Amplitude Equation for the Dynamics of Modulated Waves in the Two-Dimensional Lossless Electric Network
5.1.3 Computational Simulations
5.2 Coherent Structures for a Multi-coupled Nonlinear Transmission Network with Dissipative Elements
5.2.1 Introduction
5.2.2 Amplitude Equation for a Two-Dimensional Lossy Network
5.2.3 Modulational Instability in a Two-Dimensional Lossy Transmission Network
5.2.4 Coherent Structures for a Two-Dimensional Lossy Nonlinear Transmission Network
5.3 Soliton Signals in an Alternate Right-Handed and Left-Handed Multi-coupled Lossy Nonlinear Transmission Network
5.3.1 Description of the Model and Basic Equations
5.3.2 Complex Ginzburg-Landau Equation for the Dynamics of Modulated Waves in a Multi-coupled Lossy Network
5.3.3 Linear Stability Analysis: Modulational Instability of Stokes Waves
5.3.4 Dissipative Effects on Electrical Modulated Wave Propagation
5.3.5 Conclusion and Discussion
References
Part II Dynamics of Matter-Wave and Magnetic-Wave Solitons
6 Introduction
References
7 Dynamics of One-Dimensional Condensates with Time Modulation of the Scattering Length and Trapping Potential
7.1 Non-autonomous Solitons in Bose-Einstein Condensates …
7.1.1 Introduction
7.1.2 Cubic Inhomogeneous Nonlinear Schrödinger Equation
7.1.3 Matter-Wave Solitons in an Inhomogeneous Nonlinear Schrödinger Equation with the Spatiotemporal HO Potential
7.1.4 Conclusion
7.2 Soliton Management (SM) in One-Dimensional Bose-Einstein …
7.2.1 Introduction
7.2.2 Modulational Instability in Bose-Einstein Condensates Trapped in a Spatiotemporal-Dependent Dissipative Potential
7.2.3 Soliton Management in Bose-Einstein Condensate Systems with Two- and Three-Body Interactions Trapped in a Spatiotemporal-Dependent Dissipative Potential
7.2.4 Conclusion and Discussions
7.3 Chirped Solitons and Chirped Double-Kink Solitons …
7.3.1 Introduction
7.3.2 Derivation of the Higher-Order Nonlinear Schrödinger Equation
7.3.3 Dynamics of Chirped Femtosecond Solitons and Chirped Double-Kink Solitons in Bose-Einstein Condensates with Time-Dependent Atomic Scattering Length in a Complex Potential
7.3.4 Conclusion and Discussions
References
8 Rogue Matter Waves in Bose-Einstein Condensates Trapped in Time-Varying External Potentials
8.1 Non-autonomous Rogue Matter Waves in Bose-Einstein…
8.1.1 Introduction
8.1.2 Model and Analytical Exact First- and Second-Order Rational Solutions of the Gross-Pitaevskii Equation
8.1.3 Management of Dissipative Rogue Matter Waves in Bose-Einstein Condensates with Complicated Potential
8.1.4 Conclusion and Discussions
8.2 Chirped Rogue Matter Waves in Bose-Einstein Condensates…
8.2.1 Introduction
8.2.2 Phase Engineering and Chirped Wave Solutions
8.2.3 Evolution of Chirped Rogue Waves Under the Action of the Time-Dependent Atomic Scattering Length and Parabolic Potential
8.2.4 Conclusion and Discussions
References
9 Dynamics of Matter-Wave Solitons in Multi-component Bose-Einstein Condensates
9.1 Soliton Management in a Binary Bose-Einstein Condensate
9.1.1 The Model and Analysis
9.1.2 Results
9.1.3 Conclusion and Discussions
9.2 Soliton Stability in Binary Bose-Einstein Condensate Under Temporal Modulation
9.2.1 The Physical Model and the Lax Pair
9.2.2 Analytical and Numerical Results for Two-Component Bright Solitons in the Integrable System
9.2.3 Conclusion
References
10 Dynamics of Higher-Dimensional Condensates with Time Modulated Nonlinearity
10.1 Dynamics of Two- and Three-Dimensional Bose-Einstein …
10.1.1 The Model and Variational Approximation (VA)
10.1.2 Two-Dimensional Case
10.1.3 The Three-Dimensional Gross-Pitaevskii Model
10.1.4 Conclusion and Discussions
10.2 Stable Vortex Modes in Two-Dimensional Bose-Einstein Condensates
10.2.1 Model Description and Main Transformation
10.2.2 Exact Vortex-Soliton Solutions for the Attractive Nonlinearity (g0<0) when E=0
10.2.3 Exact Analytical Vortex-Soliton Solutions for the Repulsive Nonlinearity (g0>0)
10.2.4 Conclusion
References
11 Engineering Matter-Wave Solitons in Spinor Bose-Einstein Condensates
11.1 Formulation of the Model
11.2 Exact Analytical One-, Two-, and Three-Component Soliton Solutions
11.2.1 Single-Component FM Solitons
11.2.2 Single-Component Polar Solitons
11.2.3 Two-Component Polar Solitons
11.2.4 Three-Component Polar Solitons
11.2.5 Multistability of Solitons
11.2.6 Finite-Background Solitons
11.3 The Darboux Transform and Nonlinear Development of Modulational Instability
11.4 Conclusion
References
12 Engineering Magnetic Solitons in Nonlinear Systems
12.1 Dynamics of Dissipative Magnetic Matter-Wave Solitons in a Spinor …
12.1.1 Introduction and Model Equations
12.1.2 Exact Analytical Solutions and Dissipative Magnetic Polariton Solitons in a Spinor Polariton Bose-Einstein Condensate
12.1.3 Conclusion and Discussions
12.2 Nonlinear Magnetization Dynamics of a Classical Ferromagnet
12.2.1 Introduction
12.2.2 Macroscopic Description and Equation of Motion
12.2.3 Soliton Solutions
12.2.4 Asymptotic Behavior of Multisoliton Solutions
12.2.5 Conclusion
12.3 Nonlinear Magnetization Dynamics in the Presence of Spin-Polarized Current
12.3.1 Introduction
12.3.2 Long Ferromagnetic Nanowire with a Uniform Cross Section (High-Q Model, Q>1)
12.3.3 Short Ferromagnetic Nanowire with a Uniform Cross Section (Low-Q Model, Q<1)
12.3.4 Conclusion
References
13 Current Driven Dynamics of Magnetization in Ferromagnet with Spin Transfer Torque
13.1 Introduction
13.2 Current Driven Dynamics of Domain Wall in Ferrimagnets
13.2.1 Domain-Wall Resonance Induced by Spin-Polarized Current
13.2.2 Screw-Pitch Effect and Velocity Oscillation of Domain Wall
13.2.3 Non-autonomous Helical Motion of Magnetization in Ferromagnetic Nanowire
13.3 Current Driven Dynamics of Soliton
13.3.1 Dark Solitons
13.3.2 Bright Soliton
13.3.3 Current Driven Interaction of Spin Wave and Soliton
13.3.4 Dynamics of Magnetic Rogue Wave
13.4 Ferromagnetic Resonance in Magnetic Trilayers
13.4.1 Ferromagnetic Resonance in a Perpendicular-Analyzer Magnetic Trilayer
13.4.2 Stability Analysis of Perpendicular Magnetic Trilayers
13.5 Conclusion
References
Index
