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.

Exponential Localization Versus Soliton Propagation.- Pulse Confinement in Optical Fibers with Random Dispersion.- Propagation of an Optical Pulse in a Fiber with Random Dispersion - management.- Spatial Solitons in Random Quadratic Media.- Correlation of the Amplitude and Phase Random Modulations in Nonlinear Medium.- Spatio-temporal Chaos in Time Evolution of BEC with Attractive Two-body Interactions.- Dynamics of a Bose-Einstein Condensate in Optical Trap.- Aspects of Discrete Breathers and New Directions.- Complexity at Mesoscale.- Resonant Mode Interactions in Nonlinear Lattices.- Discrete Solitons in Nonlinear Waveguide Arrays.- Quantization of Intrinsic Nonlinear Localized Modes in Solids.- Experiments with Discrete Breathers in Josephson Arrays.- Breather Compactification in Nonlinear Anharmonic Lattices with Nonlocal Dispersive Interactions.- Growth and Decay of Weakly Perturbed Discrete Breathers.- Standing Waves in ID Nonlinear Lattices.- Wannier-Stark Solitons in Waveguide Arrays with Linear Potential.- The Stimulated Raman Scattering System: a Numerical Study.- Chaotic Dynamics of Topological Defects in Parametrically Excited Waves.- Wavebreaking in Hydrodynamics of the Defocusing NLS Equation.- Propagation and Interaction of Extremely Short Electromagnetic Pulses in Non-Linear Media.- Nonlinear Impurity Modes in Homogeneous and Periodic Media.- Effects of Linear and Nonlinear Photo-elasticity in Super-lattices Near Interband Resonances.- Resonant Optics of Impurities in Photonic Crystals.- Bragg-grating Solitons in Dual-core Semi-linear Systems.- Transverse Patterns in Type-II Optical Parametric Oscillators.- Self-trapping and Localized Modes in 2-D Photonic Crystals.- Soliton Self-shaping Through Transverse Electrostrictive Modulation in a Brillouin FiberRing Laser.- Quantum Dynamics in Kerr Nonlinear Coupler via Phase-space Representation.- Exact Cluster Expansions for a One-dimensional ?-function Bose Gas.- Nonlinear Optical Shocks and Missiles. Theory, Applications and Numerical Methods.- Nonlinear Analysis of Heart Rate Variability.- Phenomenon of "Quantized" Oscillation Excitation.- The Doppler Effect and Form of the Profile of Radiation Spectral Lines.- Dissipative soliton dynamics in strongly driven ferromagnets.- Nonlinear Eigenmodes in Quadratic Film Waveguides.- Accelerating Solitons and Photorefractivity.