Ebook: Nonlinearity and Disorder: Theory and Applications

An up to date exposition of nonlinear phenomena in random and inhomogeneous media which provides recent results on the combined effects of nonlinearity and inhomogeneity, including random inhomogeneity. Topics covered include recent developments within such popular areas as nonlinear photonic crystals, inhomogeneous optical fibres (dispersion management), discrete nonlinear lattices, discrete breathers, Bose-Einstein condensates, ultra-short optical pulse, Josephson lattices, various types of inhomogeneous waveguides and nonlinear quantization.

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An up to date exposition of nonlinear phenomena in random and inhomogeneous media which provides recent results on the combined effects of nonlinearity and inhomogeneity, including random inhomogeneity. Topics covered include recent developments within such popular areas as nonlinear photonic crystals, inhomogeneous optical fibres (dispersion management), discrete nonlinear lattices, discrete breathers, Bose-Einstein condensates, ultra-short optical pulse, Josephson lattices, various types of inhomogeneous waveguides and nonlinear quantization.
Content:
Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Exponential Localization Versus Soliton Propagation....Pages 3-17
Pulse Confinement in Optical Fibers with Random Dispersion....Pages 19-28
Propagation of an Optical Pulse in a Fiber with Random Dispersion-Management....Pages 29-36
Spatial Solitons in Random Quadratic Media....Pages 37-53
Correlation of the Amplitude and Phase Random Modulations in Nonlinear Medium....Pages 55-60
Spatio-Temporal Chaos in Time Evolution of BEC with Attractive Two-Body Interactions....Pages 61-67
Dynamics of a Bose-Einstein Condensate in Optical Trap....Pages 69-78
Front Matter....Pages 79-79
Aspects of Discrete Breathers and New Directions....Pages 81-98
Complexity at Mesoscale....Pages 99-113
Resonant Mode Interactions in Nonlinear Lattices....Pages 115-130
Discrete Solitons in Nonlinear Waveguide Arrays....Pages 131-157
Quantization of Intrinsic Nonlinear Localized Modes in Solids....Pages 159-171
Experiments with Discrete Breathers in Josephson Arrays....Pages 173-187
Breather Compactification in Nonlinear Anharmonic Lattices with Nonlocal Dispersive Interactions....Pages 189-195
Growth and Decay of Weakly Perturbed Discrete Breathers....Pages 197-203
Standing Waves in 1D Nonlinear Lattices....Pages 205-211
Wannier-Stark Solitons in Waveguide Arrays with Linear Potential....Pages 213-220
Front Matter....Pages 221-221
The Stimulated Raman Scattering System: A Numerical Study....Pages 223-237
Chaotic Dynamics of Topological Defects in Parametrically Excited Waves....Pages 239-253
Wavebreaking in Hydrodynamics of the Defocusing NLS Equation....Pages 255-261
Front Matter....Pages 221-221
Propagation and Interaction of Extremely Short Electromagnetic Pulses in Non-Linear Media....Pages 263-278
Nonlinear Impurity Modes in Homogeneous and Periodic Media....Pages 279-289
Effects of Linear and Nonlinear Photo-Elasticity in Super-Lattices Near Interband Resonances....Pages 291-296
Resonant Optics of Impurities in Photonic Crystals....Pages 297-305
Bragg-Grating Solitons in Dual-Core Semi-Linear Systems....Pages 307-313
Transverse Patterns in Type-II Optical Parametric Oscillators....Pages 315-322
Self-Trapping and Localized Modes in 2D Photonic Crystals....Pages 323-330
Soliton Self-Shaping through Transverse Electrostrictive Modulation in a Brillouin Fiber Ring Laser....Pages 331-340
Quantum Dynamics in Kerr Nonlinear Coupler Via Phase-Space Representation....Pages 341-349
Exact Cluster Expansions for a One-Dimensional ?-Function Bose Gas....Pages 351-361
Front Matter....Pages 363-363
Nonlinear Optical Shocks and Missiles. Theory, Applications and Numerical Methods....Pages 365-385
Nonlinear Analysis of Heart Rate Variability....Pages 387-395
Phenomenon of “Quantized” Oscillation Excitation....Pages 397-409
The Doppler Effect and Form of the Profile of Radiation Spectral Lines....Pages 411-414
Dissipative Soliton Dynamics in Strongly Driven Ferromagnets....Pages 415-422
Nonlinear Eigenmodes in Quadratic Film Waveguides....Pages 423-433
Accelerating Solitons and Photorefractivity....Pages 435-441
Back Matter....Pages 443-445

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An up to date exposition of nonlinear phenomena in random and inhomogeneous media which provides recent results on the combined effects of nonlinearity and inhomogeneity, including random inhomogeneity. Topics covered include recent developments within such popular areas as nonlinear photonic crystals, inhomogeneous optical fibres (dispersion management), discrete nonlinear lattices, discrete breathers, Bose-Einstein condensates, ultra-short optical pulse, Josephson lattices, various types of inhomogeneous waveguides and nonlinear quantization.
Content:
Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Exponential Localization Versus Soliton Propagation....Pages 3-17
Pulse Confinement in Optical Fibers with Random Dispersion....Pages 19-28
Propagation of an Optical Pulse in a Fiber with Random Dispersion-Management....Pages 29-36
Spatial Solitons in Random Quadratic Media....Pages 37-53
Correlation of the Amplitude and Phase Random Modulations in Nonlinear Medium....Pages 55-60
Spatio-Temporal Chaos in Time Evolution of BEC with Attractive Two-Body Interactions....Pages 61-67
Dynamics of a Bose-Einstein Condensate in Optical Trap....Pages 69-78
Front Matter....Pages 79-79
Aspects of Discrete Breathers and New Directions....Pages 81-98
Complexity at Mesoscale....Pages 99-113
Resonant Mode Interactions in Nonlinear Lattices....Pages 115-130
Discrete Solitons in Nonlinear Waveguide Arrays....Pages 131-157
Quantization of Intrinsic Nonlinear Localized Modes in Solids....Pages 159-171
Experiments with Discrete Breathers in Josephson Arrays....Pages 173-187
Breather Compactification in Nonlinear Anharmonic Lattices with Nonlocal Dispersive Interactions....Pages 189-195
Growth and Decay of Weakly Perturbed Discrete Breathers....Pages 197-203
Standing Waves in 1D Nonlinear Lattices....Pages 205-211
Wannier-Stark Solitons in Waveguide Arrays with Linear Potential....Pages 213-220
Front Matter....Pages 221-221
The Stimulated Raman Scattering System: A Numerical Study....Pages 223-237
Chaotic Dynamics of Topological Defects in Parametrically Excited Waves....Pages 239-253
Wavebreaking in Hydrodynamics of the Defocusing NLS Equation....Pages 255-261
Front Matter....Pages 221-221
Propagation and Interaction of Extremely Short Electromagnetic Pulses in Non-Linear Media....Pages 263-278
Nonlinear Impurity Modes in Homogeneous and Periodic Media....Pages 279-289
Effects of Linear and Nonlinear Photo-Elasticity in Super-Lattices Near Interband Resonances....Pages 291-296
Resonant Optics of Impurities in Photonic Crystals....Pages 297-305
Bragg-Grating Solitons in Dual-Core Semi-Linear Systems....Pages 307-313
Transverse Patterns in Type-II Optical Parametric Oscillators....Pages 315-322
Self-Trapping and Localized Modes in 2D Photonic Crystals....Pages 323-330
Soliton Self-Shaping through Transverse Electrostrictive Modulation in a Brillouin Fiber Ring Laser....Pages 331-340
Quantum Dynamics in Kerr Nonlinear Coupler Via Phase-Space Representation....Pages 341-349
Exact Cluster Expansions for a One-Dimensional ?-Function Bose Gas....Pages 351-361
Front Matter....Pages 363-363
Nonlinear Optical Shocks and Missiles. Theory, Applications and Numerical Methods....Pages 365-385
Nonlinear Analysis of Heart Rate Variability....Pages 387-395
Phenomenon of “Quantized” Oscillation Excitation....Pages 397-409
The Doppler Effect and Form of the Profile of Radiation Spectral Lines....Pages 411-414
Dissipative Soliton Dynamics in Strongly Driven Ferromagnets....Pages 415-422
Nonlinear Eigenmodes in Quadratic Film Waveguides....Pages 423-433
Accelerating Solitons and Photorefractivity....Pages 435-441
Back Matter....Pages 443-445
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