front-matter
Chapter 1
Dissipative Solitons in the Complex Ginzburg-Landauand Swift-Hohenberg Equations
N. Akhmediev and A. Ankiewicz
1 What are Dissipative Solitons?
2 Mathematical Model
3 Are there Integrable Dissipative Systems?
4 Stationary Solitons as Fixed Points
5 Stability Analysis
6 Energy Flow Across a Soliton
7 Pulsating Soliton as a Limit Cycle
8 Period Doubling of Pulsating Solitons
9 Chaotic Soliton as a Strange Attractor
10 Soliton Explosions
11 Spectrum of Eigenvalues
12 Global Dynamics of the Exploding Soliton
13 Conclusion
References
Chapter 2
Dissipative Magneto-Optic Solitons
A.D. Boardman, L. Velasco, and P. Egan
1 Introduction
2 The Basic Cubic-Quintic ComplexGinzburg-Landau Equation
3 Magneto-Optics with Inhomogeneous Magnetisation
4 Dissipative Solitons in Voigt Configuration
5 Optical Singularities in Dissipative Media
References
Chapter 3
Dissipative Solitons in Semiconductor Optical Amplifiers
E. Ultanir, G.I. Stegeman, D. Michaelis, C.H. Lange, and F. Lederer
1 Introduction
2 Solitons in Uniformly-Pumped SOAs
3 Theory of Solitons in Periodically-Pumped SOAs
4 Sample Fabrication
5 Experiment Results
6 Soliton Interactions
7 Conclusion
References
Chapter 4
Dissipative Solitons in Pattern-Forming Nonlinear Optical Systems: Cavity Solitons and Feedback Solitons
T. Ackemann and W.J. Firth
1 Introduction
2 History
3 Mean-Field Models and Cavity Solitons
4 Self-Propelled Cavity Solitons in Semiconductor Microresonators
5 Solitons in a Single-Mirror Feedback Arrangement
6 Basic Results
7 Interaction Behavior
8 Applications
9 Conclusion
References
Chapter 5
Solitons in Laser Systems with Saturable Absorption
N.N. Rosanov
1 Introduction: Definitions, Examples, History
2 Model and Evolution Equation
3 Stationary Symmetric Solitons
4 Two-Dimensional Laser Solitons
5 Numerical Simulations of Asymmetric Solitons
6 Energy Flows and Soliton Internal Structure
7 Effect of Frequency Detunings and Bio-Solitons
References
Chapter 6
Spatial Resonator Solitons
V.B. Taranenko, G. Slekys, and C.O. Weiss
1 Introduction: A Multi-Disciplinary Viewof Pattern Formation and Solitons
2 Proof-of-Existence Experimentson Resonator Solitons with Slow Materials
3 Semiconductor Resonator Solitons
4 Conclusion
References
Chapter 7
Dynamics of Dissipative Temporal Solitons
U. Peschel, D. Michaelis, Z. Bakonyi, G. Onishchukov, and F. Lederer
1 Introduction
2 Mathematical Models
3 Solutions and Their Stability
4 Soliton Experiments
5 Soliton Dynamics
6 Conclusions
References
Chapter 8
Soliton Dynamics in Mode-Locked Lasers
S.T. Cundiff
1 Mode-Locked Laser Basics
2 Soliton Polarization Evolution
3 Soliton Explosions
4 Carrier-Envelope Phase
5 Summary
References
Chapter 9
Temporal Multi-Soliton Complexes Generatedby Passively Mode-Locked Lasers
J.M. Soto-Crespo and Ph. Grelu
1 Introduction
2 Experimental Evidencefor Multi-Soliton Formationin Passively Mode-Locked Laser Cavities
3 Multi-Soliton Complexesin Various Fiber Laser Configurations
4 Multi-Soliton Complexes in Distributed Models
5 Non-Distributed Model
6 Conclusions
References
Chapter 10
Mode-Locking of Fiber Lasers via Nonlinear Mode-Coupling
J.N. Kutz
1 Introduction
2 Master Mode-Locking
3 Mode-Locking via Nonlinear Mode-Coupling
4 Conclusions and Discussion
References
Chapter 11
Dissipative Solitons in Reaction-Diffusion Systems
H.-G. Purwins, H.U. BΓΆdeker, and A.W. Liehr
1 Introduction
2 Mechanism of Pattern Formationin Reaction-Diffusion Systems
3 Numerical Investigations of the Three-Component System
4 Analytical Investigations
5 Planar Gas-Discharge Systems as Reaction-Diffusion Systems
6 Conclusion
References
Chapter 12
Discrete Ginzburg-Landau Solitons
N.K. Efremidis and D.N. Christodoulides
1 Introduction
2 Formulation
3 Linear Properties
4 Nonlinear Properties
References
Chapter 13
Discrete Dissipative Solitons
F.Kh. Abdullaev
1 Introduction
2 Model and Basic Equations
3 Exact Localized Solutions of DCGL Equation
4 Conclusion
References
Chapter 14
Nonlinear Schrodinger Equation with Dissipation:Two Models for Bose-Einstein Condensates
V.V. Konotop
1 Introduction
2 From a Three-Dimensional Gross-Pitaevskii Equation to the One-Dimensional Nonlinear SchrΓΆdinger Equation
3 Periodic Solutions
4 Management of Matter Waves Usingthe Feshbach Resonance
5 BEC in an Optical Lattice Controlledby the Feshbach Resonance
6 Modulation Instability of BEC in a Parabolic Trap
7 Concluding Remarks
References
Chapter 15
Solitary Waves of Nonlinear Nonintegrable Equations
R. Conte and M. Musette
1 Introduction
2 The Known Solutions of the Examples
3 Investigation of the Amount of Integrability
4 Selection of Possibly Single-ValuedDependent Variables
5 On the Cost of Obtaining Closed Form Expressions
6 First Class of Methods: Truncations
7 Second Class of Methods: First-Order Sub-Equation
8 Conclusion
9 Appendix. Classical Resultson First-Order Autonomous Equations
References
Chapter 16
Stability Analysis of Pulses via the Evans Function: Dissipative Systems
T. Kapitula
1 Introduction
2 Basic Example
3 Construction of the Evans Function
4 The Linearizationof the Nonlinear SchrΓΆdinger Equation
5 Dissipative Perturbations
References
Chapter 17
Bifurcations and Strongly Amplitude-Modulated Pulsesof the Complex Ginzburg-Landau Equation
S.R. Choudhury
1 Introduction
2 Background Properties of Coherent Structuresof the CGLE Equation
3 Numerical Pulse Solutions
4 Bifurcations in the CGLEand Various Theoretical Approaches
5 Summary
References
back-matter