Nonlinear Waves: Classical and Quantum Aspects

Leading scientists discuss the most recent physical and experimental results in the physics of Bose-Einstein condensate theory, the theory of nonlinear lattices (including quantum and nonlinear lattices), and nonlinear optics and photonics. Classical and quantum aspects of the dynamics of nonlinear waves are considered. The contributions focus on the Gross-Pitaevskii equation and on the quantum nonlinear Schrödinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.

Contenu
Nonlinear Systems. General Topics.- Towards Algebro-Geometric Integration of the Gross-Pitaevskii Equation.- On Modeling Adiabatic N-Soliton Interactions.- Dynamical Stabilization of nonlinear Waves.- Solitons as Strange Attractors.- Multidimensional Solitons and Vortices in Periodic Potentials.- Globally-Linked Vortex Clusters.- Solutions of the Logarithmic Schrödinger Equation in a Rotating Harmonic Trap.- Linear and Nonlinear Bound States in Curved Waveguides.- Numerical Study of a Nonlocal Sine-Gordon Equation.- A Fruitful Interplay: From Nonlocality to Fractional Calculus.- On 3+1 Dimensional Friedman-Robertson-Walker Universes with Matter.- Stochastic Effects on the Eckhaus Equation.- Modulational Instability of Some Nonlinear Continuum and Discrete Models.- Scattering of NLS Solitons with Bound Quantum States.- Oscillator-Wave Model: Multiple Attractors and Strong Stability.- Bose-Einstein Condensates and Matter Waves.- Bose-Einstein Condensation: The Odd Nonlinear Quantum Mechanics.- Statistical Mechanics of Quantum Integrable Systems.- Bose-Einstein Condensates in an Optical Lattice.- Bose-Einstein Condensates in Optical Lattices in the Nonlinear Regime.- Quantum Bound States and Matter Waves Delocalizations.- Control of Matter Waves in Optical Lattices by Feshbach Resonance.- Two-Component Bose-Einstein Condensates in Optical Lattices.- Shock Waves in Bose-Einstein Condensates.- Nonlinear Optics and Photonics.- Stopping and Bending Light in 2D Photonic Structures.- Model of the Two Level Quantum Dots Ensemble Interacting with Ultra-Short Pulse of Coherent Radiation.- Enhanced Optical Transmission Via Tunnel Coupling in Surface Polaritonic Crystals.- Liquid Light in Cubic-Quintic Nonlinear Optical Materials.- Optical Pulse Evolution Toward Light Bulletand Vortex Solution.- The Description of Extremely Short Pulses in Non-Resonant Media in Frame of Maxwell-Duffing-Type Models.- Statistics of Three Interacting Optical Solitons.- Statistical Study of Raman Scattering in Optical Fibers Affected by Random Conditions.- Electromagnetics of Unharmonic Waves Exactly Solvable Models.- Nonlinear Waves in Discrete Systems.- Quantum Breathers in an Attractive Fermionic Hubbard Model.- Energy Localization and First Order Phase Transition in Solids and Molecules.- Soliton Dynamics in Randomly Perturbed Discrete Lattices.- Ultrafast Electron Transfer: the Standard Theory Revisited.- Nonlinear Spectroscopy Study of Vibrational Self-Trapping in Hydrogen Bonded Crystals.- Quantum Anharmonic Phonons in the Fermi-Pasta-Ulam Chain.- Dynamics of the Perturbed Ablowitz-Ladik Soliton Beyond the Adiabatic Approximation.- Travelling Waves in a Perturbed Discrete Sine-Gordon Equation.- Dynamics of Multicomponent Solitons in Perturbed Ladder Lattices.- Miwa's Representation of the Volterra Hierarchy.- Moving Topological Solitons in the Discrete Klein-Gordon Equation.- Dynamics of Discrete Solitons in Media with Varying Nonlinearity.- On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains.- On the Geometry of Stationary Heisenberg Ferromagnets.