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Three Sources and Three Component Parts of the Concept of Dissipative Solitons | |
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Introduction | |
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Cubic-Quintic Complex Ginzburg-Landau Equation | |
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The Method of Moments | |
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Pulsating Solitons and Their Approximations [37, 38] | |
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Creeping Solitons [32, 43] | |
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Solitons and Antisolitons [28] | |
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Conclusions | |
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References | |
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Solitons in Viscous Flows | |
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Introduction | |
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Basic Models | |
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Marangoni Waves | |
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Waves in Flowing Films | |
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Conclusions | |
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References | |
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Cavity Solitons in Semiconductor Devices | |
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Introduction | |
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Cavity Solitons: Properties and Applicative Features | |
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Cavity Solitons in Driven VCSELs | |
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VCSELs with Saturable Absorber: The Cavity Soliton Laser | |
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Conclusions and Perspectives | |
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References | |
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Dissipative Solitons in Laser Systems with Non-local and Non-instantaneous Nonlinearity | |
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Introduction | |
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The Model and Initial Equations | |
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Transversely Homogeneous Lasing | |
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Single Motionless Dissipative Solitons and Their Complexes | |
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Bifurcation from Motionless to Slowly Moving Structures | |
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Slowly Moving Dissipative Solitons | |
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Flying and Non-stationary Dissipative Solitons | |
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Conclusions | |
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References | |
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Excitability Mediated by Dissipative Solitons in Nonlinear Optical Cavities | |
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Introduction | |
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Model | |
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Dissipative Solitons for Homogeneous Pump | |
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Azimuthal Instabilities | |
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Oscillatory KCSs | |
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Saddle-Loop Bifurcation | |
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Quantitative Phase Space Projection | |
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Excitable Behavior | |
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Takens-Bogdanov Point | |
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Effect of an Addressing Gaussian Beam | |
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Concluding Remarks | |
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References | |
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Temporal Soliton "Molecules" in Mode-Locked Lasers: Collisions, Pulsations, and Vibrations | |
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Introduction | |
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Collisions Between Dissipative Solitons Inside a Laser Cavity | |
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Pulsations of Dissipative Solitons | |
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Vibrations of a Soliton Pair | |
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Conclusion and Prospects | |
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References | |
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Compounds of Fiber-Optic Solitons | |
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Introduction | |
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General | |
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Soliton Ensembles in a Feedback System | |
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Soliton Molecules: Bound States in Dispersion-Managed Fiber | |
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Bound States of Dark Solitons in Dispersion-Managed Fiber | |
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Discussion and Conclusion | |
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References | |
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Dissipative Nonlinear Structures in Fiber Optics | |
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Introduction | |
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Dissipative Solitons in High-Speed Fiber Communication Systems | |
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Self-Similar Parabolic Pulses in Active Fibers | |
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Application of Parabolic Pulses to Optical Signal Processing | |
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Conclusion | |
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References | |
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Three-Wave Dissipative Brillouin Solitons | |
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Introduction | |
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SBS Kerr Model Equations | |
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Three-Wave Dissipative Model | |
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Asymptotic Three-Wave Dynamics in the Ring Cavity | |
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Backward-Traveling Three-Wave Solutions | |
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Dissipative Symmetric Three-Wave Solution | |
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Asymmetric Three-Wave Dissipative Solitons | |
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Stability Criterion: Asymptotic Procedure | |
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Brillouin Fiber-Ring Laser Pulses | |
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Systematic Experimental and Numerical Exploration of the Whole Soliton Localization Domain | |
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Conclusion | |
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References | |
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Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators | |
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Introduction | |
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Convective Versus Absolute Instabilities in OPOs | |
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Degenerate Optical Parametric Oscillators | |
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Walk-Off Nonlinear Effects in Parametric Optical Oscillators | |
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Concluding Remarks | |
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References | |
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Discrete Breathers with Dissipation | |
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Introduction | |
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Basic Properties of Discrete Breathers | |
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Applications | |
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Summary | |
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References | |
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Anharmonic Oscillations, Dissipative Solitons and Non-Ohmic Supersonic Electric Transport | |
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Introduction | |
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Solitons and Cnoidal Waves in a Toda Lattice | |
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Self-Organization with an Input-Output Energy Balance | |
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Electromechanical Toda Lattice | |
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From Ohm's Law to a Soliton-Mediated Supersonic Current | |
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Final Remarks | |
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References | |
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Coherent Optical Pulse Dynamics in Nano-composite Plasmonic Bragg Gratings | |
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Introduction | |
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Basic Equations | |
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Solitary Wave Solutions | |
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Energy Partition | |
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Numerical Simulation | |
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Conclusion | |
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References | |
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Collective Focusing and Modulational Instability of Light and Cold Atoms | |
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Introduction | |
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Dynamical Equations | |
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Coupled Optical and Atomic Solitons | |
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Two-Beam Coupling and Atomic Density Perturbations | |
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Modulational Instability | |
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Modulational Instability with Density Changes | |
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Experimental Observations | |
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Conclusion | |
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References | |
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On Vegetation Clustering, Localized Bare Soil Spots and Fairy Circles | |
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Introduction | |
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Mean-Field Model of Vegetation Evolution | |
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Weak-Gradient Approximation | |
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Clustering and Periodic Vegetation Patterns | |
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Pinning and Localized Bare Soil Spots | |
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Attractive/Repulsive Interactions Between Bare spots | |
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Conclusions | |
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References | |
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Propagation of Traveling Pulses in Cortical Networks | |
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Introduction | |
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Propagating Pulses in Networks of Excitatory Neurons | |
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Propagating Pulses in Networks of Excitatory and Inhibitory Neurons | |
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Discussion | |
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References | |
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Wave Phenomena in Neuronal Networks | |
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Introduction | |
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Traveling Waves | |
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Wave Fronts | |
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Solitary Traveling Waves | |
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Multi-bump Waves | |
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Two Dimensions | |
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Conclusions | |
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References | |
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Spiral Waves and Dissipative Solitons in Weakly Excitable Media | |
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Introduction | |
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Excitable Medium Model | |
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Free Boundary Problem for Stabilized Wave Segments | |
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Wave Spots Rotating Along a Disk Boundary | |
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Spiral Waves Rotating Around a Disk Center | |
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Spiral Waves in an Unbounded Medium | |
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Discussion | |
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References | |
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Index | |