Contents Three Sources and Three Component Parts of the Concept of Dissipative Solitons Solitons in Viscous Flows

Transcription

1 Three Sources and Three Component Parts of the Concept of Dissipative Solitons... 1 N. Akhmediev and A. Ankiewicz 1 Introduction Cubic-Quintic Complex Ginzburg Landau Equation TheMethodofMoments PulsatingSolitonsandTheirApproximations[37,38] Creeping Solitons [32, 43] SolitonsandAntisolitons[28] Conclusions References Solitons in Viscous Flows M.G. Velarde and A.A. Nepomnyashchy 1 Introduction Basic Models Marangoni Waves WavesinFlowingFilms Conclusions References Cavity Solitons in Semiconductor Devices L.A. Lugiato, F. Prati, G. Tissoni, M. Brambilla, S. Barland, M. Giudici, and J.R. Tredicce 1 Introduction Cavity Solitons: Properties and Applicative Features CavitySolitonsinDrivenVCSELs VCSELs with Saturable Absorber: The Cavity Soliton Laser Conclusions and Perspectives References ix

2 x Contents Dissipative Solitons in Laser Systems with Non-local and Non-instantaneous Nonlinearity N.N. Rosanov, S.V. Fedorov, and A.N. Shatsev 1 Introduction The Model and Initial Equations Transversely Homogeneous Lasing SingleMotionlessDissipativeSolitonsandTheirComplexes BifurcationfromMotionlesstoSlowlyMovingStructures SlowlyMovingDissipativeSolitons Flying and Non-stationary Dissipative Solitons Conclusions References Excitability Mediated by Dissipative Solitons in Nonlinear Optical Cavities P. Colet, D. Gomila, A. Jacobo, and M.A. Matías 1 Introduction Model Dissipative Solitons for Homogeneous Pump Azimuthal Instabilities Oscillatory KCSs Saddle-Loop Bifurcation Quantitative Phase Space Projection ExcitableBehavior Takens Bogdanov Point EffectofanAddressingGaussianBeam Concluding Remarks References Temporal Soliton Molecules in Mode-Locked Lasers: Collisions, Pulsations, and Vibrations P. Grelu and J.M. Soto-Crespo 1 Introduction Collisions Between Dissipative Solitons Inside a Laser Cavity PulsationsofDissipativeSolitons Vibrations of a Soliton Pair Conclusion and Prospects References Compounds of Fiber-Optic Solitons F. Mitschke 1 Introduction General Soliton Ensembles in a Feedback System Soliton Molecules: Bound States in Dispersion-Managed Fiber Bound States of Dark Solitons in Dispersion-Managed Fiber

3 xi 6 Discussion and Conclusion References Dissipative Nonlinear Structures in Fiber Optics S.K. Turitsyn and S. Boscolo 1 Introduction Dissipative Solitons in High-Speed Fiber Communication Systems Self-SimilarParabolicPulsesinActiveFibers Application of Parabolic Pulses to Optical Signal Processing Conclusion References Three-Wave Dissipative Brillouin Solitons C. Montes 1 Introduction SBS Kerr Model Equations Three-Wave Dissipative Model Asymptotic Three-Wave Dynamics in the Ring Cavity Backward-Traveling Three-Wave Solutions DissipativeSymmetricThree-WaveSolution AsymmetricThree-WaveDissipativeSolitons Stability Criterion: Asymptotic Procedure BrillouinFiber-RingLaserPulses Systematic Experimental and Numerical Exploration of the Whole Soliton Localization Domain Conclusion References Spatial Dissipative Solitons Under Convective and Absolute Instabilities in Optical Parametric Oscillators S. Coulibaly, C. Durniak, and M. Taki 1 Introduction Convective Versus Absolute Instabilities in OPOs Degenerate Optical Parametric Oscillators Walk-Off Nonlinear Effects in Parametric Optical Oscillators Concluding Remarks References Discrete Breathers with Dissipation S. Flach and A.V. Gorbach 1 Introduction Basic Properties of Discrete Breathers Applications Summary References

4 xii Contents Anharmonic Oscillations, Dissipative Solitons and Non-Ohmic Supersonic Electric Transport M.G. Velarde, W. Ebeling, and A.P. Chetverikov 1 Introduction Solitons and Cnoidal Waves in a Toda Lattice Self-Organization with an Input Output Energy Balance Electromechanical Toda Lattice From Ohm s Law to a Soliton-Mediated Supersonic Current FinalRemarks References Coherent Optical Pulse Dynamics in Nano-composite Plasmonic Bragg Gratings I.R. Gabitov, A.O. Korotkevich, A.I. Maimistov, and J.B. McMahon 1 Introduction BasicEquations Solitary Wave Solutions Energy Partition NumericalSimulation Conclusion References Collective Focusing and Modulational Instability of Light and Cold Atoms M. Saffman and Y. Wang 1 Introduction Dynamical Equations Coupled Optical and Atomic Solitons Two-BeamCouplingandAtomicDensityPerturbations Modulational Instability Modulational Instability with Density Changes Experimental Observations Conclusion References On Vegetation Clustering, Localized Bare Soil Spots and Fairy Circles M. Tlidi, R. Lefever, and A. Vladimirov 1 Introduction Mean-Field Model of Vegetation Evolution Weak-Gradient Approximation ClusteringandPeriodicVegetationPatterns Pinning and Localized Bare Soil Spots Attractive/Repulsive Interactions Between Bare Spots Conclusions References

5 xiii Propagation of Traveling Pulses in Cortical Networks D. Golomb 1 Introduction Propagating Pulses in Networks of Excitatory Neurons Propagating Pulses in Networks of Excitatory andinhibitoryneurons Discussion References Wave Phenomena in Neuronal Networks W.C. Troy 1 Introduction TravelingWaves WaveFronts Solitary Traveling Waves Multi-bump Waves TwoDimensions Conclusions References Spiral Waves and Dissipative Solitons in Weakly Excitable Media V.S. Zykov 1 Introduction Excitable Medium Model Free Boundary Problem for Stabilized Wave Segments Wave Spots Rotating Along a Disk Boundary Spiral Waves Rotating Around a Disk Center Spiral Waves in an Unbounded Medium Discussion References Index...475