Ebook: 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.

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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 Schr?dinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.

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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 Schr?dinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Content:
Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Towards Algebro-Geometric Integration of the Gross-Pitaevskii Equation....Pages 3-14
On Modeling Adiabatic N-Soliton Interactions....Pages 15-28
Dynamical Stabilization of nonlinear Waves....Pages 29-44
Solitons as Strange Attractors....Pages 45-60
Multidimensional Solitons and Vortices in Periodic Potentials....Pages 61-80
Globally-Linked Vortex Clusters....Pages 81-98
Solutions of the Logarithmic Schr?dinger Equation in a Rotating Harmonic Trap....Pages 99-106
Linear and Nonlinear Bound States in Curved Waveguides....Pages 107-120
Numerical Study of a Nonlocal Sine-Gordon Equation....Pages 121-128
A Fruitful Interplay: From Nonlocality to Fractional Calculus....Pages 129-133
On 3+1 Dimensional Friedman-Robertson-Walker Universes with Matter....Pages 135-143
Stochastic Effects on the Eckhaus Equation....Pages 145-150
Modulational Instability of Some Nonlinear Continuum and Discrete Models....Pages 151-156
Scattering of NLS Solitons with Bound Quantum States....Pages 157-162
“Oscillator-Wave” Model: Multiple Attractors and Strong Stability....Pages 163-171
Front Matter....Pages 173-173
Bose-Einstein Condensation: The Odd Nonlinear Quantum Mechanics....Pages 175-192
Statistical Mechanics of Quantum Integrable Systems....Pages 193-207
Bose-Einstein Condensates in an Optical Lattice....Pages 209-222
Bose-Einstein Condensates in Optical Lattices in the Nonlinear Regime....Pages 223-236
Quantum Bound States and Matter Waves Delocalizations....Pages 237-250
Front Matter....Pages 173-173
Control of Matter Waves in Optical Lattices by Feshbach Resonance....Pages 251-267
Two-Component Bose-Einstein Condensates in Optical Lattices....Pages 269-283
Shock Waves in Bose-Einstein Condensates....Pages 285-290
Front Matter....Pages 291-291
Stopping and Bending Light in 2D Photonic Structures....Pages 293-302
Model of the Two Level Quantum Dots Ensemble Interacting with Ultra-Short Pulse of Coherent Radiation....Pages 303-312
Enhanced Optical Transmission Via Tunnel Coupling in Surface Polaritonic Crystals....Pages 313-326
Liquid Light in Cubic-Quintic Nonlinear Optical Materials....Pages 327-351
Optical Pulse Evolution Toward Light Bullet and Vortex Solution....Pages 353-359
The Description of Extremely Short Pulses in Non-Resonant Media in Frame of Maxwell-Duffing-Type Models....Pages 361-372
Statistics of Three Interacting Optical Solitons....Pages 373-379
Statistical Study of Raman Scattering in Optical Fibers Affected by Random Conditions....Pages 381-388
Electromagnetics of Unharmonic Waves — Exactly Solvable Models....Pages 389-395
Front Matter....Pages 397-397
Quantum Breathers in an Attractive Fermionic Hubbard Model....Pages 399-412
Energy Localization and First Order Phase Transition in Solids and Molecules....Pages 413-426
Soliton Dynamics in Randomly Perturbed Discrete Lattices....Pages 427-441
Ultrafast Electron Transfer: the Standard Theory Revisited....Pages 443-471
Nonlinear Spectroscopy Study of Vibrational Self-Trapping in Hydrogen Bonded Crystals....Pages 473-479
Quantum Anharmonic Phonons in the Fermi-Pasta-Ulam Chain....Pages 481-487
Dynamics of the Perturbed Ablowitz-Ladik Soliton Beyond the Adiabatic Approximation....Pages 489-495
Travelling Waves in a Perturbed Discrete Sine-Gordon Equation....Pages 497-501
Front Matter....Pages 397-397
Dynamics of Multicomponent Solitons in Perturbed Ladder Lattices....Pages 503-510
Miwa’s Representation of the Volterra Hierarchy....Pages 511-520
Moving Topological Solitons in the Discrete Klein-Gordon Equation....Pages 521-528
Dynamics of Discrete Solitons in Media with Varying Nonlinearity....Pages 529-534
On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains....Pages 535-542
On the Geometry of Stationary Heisenberg Ferromagnets....Pages 543-549
Back Matter....Pages 551-555

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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 Schr?dinger equation. Recent experimental results on atomic condensates and hydrogen bonded systems are reviewed. Particular attention is given to nonlinear matter waves in periodic potential.
Content:
Front Matter....Pages i-xxviii
Front Matter....Pages 1-1
Towards Algebro-Geometric Integration of the Gross-Pitaevskii Equation....Pages 3-14
On Modeling Adiabatic N-Soliton Interactions....Pages 15-28
Dynamical Stabilization of nonlinear Waves....Pages 29-44
Solitons as Strange Attractors....Pages 45-60
Multidimensional Solitons and Vortices in Periodic Potentials....Pages 61-80
Globally-Linked Vortex Clusters....Pages 81-98
Solutions of the Logarithmic Schr?dinger Equation in a Rotating Harmonic Trap....Pages 99-106
Linear and Nonlinear Bound States in Curved Waveguides....Pages 107-120
Numerical Study of a Nonlocal Sine-Gordon Equation....Pages 121-128
A Fruitful Interplay: From Nonlocality to Fractional Calculus....Pages 129-133
On 3+1 Dimensional Friedman-Robertson-Walker Universes with Matter....Pages 135-143
Stochastic Effects on the Eckhaus Equation....Pages 145-150
Modulational Instability of Some Nonlinear Continuum and Discrete Models....Pages 151-156
Scattering of NLS Solitons with Bound Quantum States....Pages 157-162
“Oscillator-Wave” Model: Multiple Attractors and Strong Stability....Pages 163-171
Front Matter....Pages 173-173
Bose-Einstein Condensation: The Odd Nonlinear Quantum Mechanics....Pages 175-192
Statistical Mechanics of Quantum Integrable Systems....Pages 193-207
Bose-Einstein Condensates in an Optical Lattice....Pages 209-222
Bose-Einstein Condensates in Optical Lattices in the Nonlinear Regime....Pages 223-236
Quantum Bound States and Matter Waves Delocalizations....Pages 237-250
Front Matter....Pages 173-173
Control of Matter Waves in Optical Lattices by Feshbach Resonance....Pages 251-267
Two-Component Bose-Einstein Condensates in Optical Lattices....Pages 269-283
Shock Waves in Bose-Einstein Condensates....Pages 285-290
Front Matter....Pages 291-291
Stopping and Bending Light in 2D Photonic Structures....Pages 293-302
Model of the Two Level Quantum Dots Ensemble Interacting with Ultra-Short Pulse of Coherent Radiation....Pages 303-312
Enhanced Optical Transmission Via Tunnel Coupling in Surface Polaritonic Crystals....Pages 313-326
Liquid Light in Cubic-Quintic Nonlinear Optical Materials....Pages 327-351
Optical Pulse Evolution Toward Light Bullet and Vortex Solution....Pages 353-359
The Description of Extremely Short Pulses in Non-Resonant Media in Frame of Maxwell-Duffing-Type Models....Pages 361-372
Statistics of Three Interacting Optical Solitons....Pages 373-379
Statistical Study of Raman Scattering in Optical Fibers Affected by Random Conditions....Pages 381-388
Electromagnetics of Unharmonic Waves — Exactly Solvable Models....Pages 389-395
Front Matter....Pages 397-397
Quantum Breathers in an Attractive Fermionic Hubbard Model....Pages 399-412
Energy Localization and First Order Phase Transition in Solids and Molecules....Pages 413-426
Soliton Dynamics in Randomly Perturbed Discrete Lattices....Pages 427-441
Ultrafast Electron Transfer: the Standard Theory Revisited....Pages 443-471
Nonlinear Spectroscopy Study of Vibrational Self-Trapping in Hydrogen Bonded Crystals....Pages 473-479
Quantum Anharmonic Phonons in the Fermi-Pasta-Ulam Chain....Pages 481-487
Dynamics of the Perturbed Ablowitz-Ladik Soliton Beyond the Adiabatic Approximation....Pages 489-495
Travelling Waves in a Perturbed Discrete Sine-Gordon Equation....Pages 497-501
Front Matter....Pages 397-397
Dynamics of Multicomponent Solitons in Perturbed Ladder Lattices....Pages 503-510
Miwa’s Representation of the Volterra Hierarchy....Pages 511-520
Moving Topological Solitons in the Discrete Klein-Gordon Equation....Pages 521-528
Dynamics of Discrete Solitons in Media with Varying Nonlinearity....Pages 529-534
On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains....Pages 535-542
On the Geometry of Stationary Heisenberg Ferromagnets....Pages 543-549
Back Matter....Pages 551-555
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