Nonlinearity and disorder : theory and applications : proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001

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. 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 δ-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 It is well-known that in one-dimensional random linear media strong localization occurs, which means in particular that the transmitted intensity decays exponentially as a function of the size of the medium [1]. Proceedings of the NATO Advanced Research Workshop, Tashkent, Uzbekistan, 2-6 October 2001