Multidimensional Solitons

Cover
Half Title
Title Page
Copyright Page
Acronyms
Preface
Table of Contents
Chapter 1: Introduction
	1.1 ONE-DIMENSIONAL SOLITONS
	1.2 EXIT TO THE MULTIDIMENSIONAL WORLD
	REFERENCES
Chapter 2: Basic Theoretical Models
	2.1 MODELS WITH COMPETING AND SATURABLE NONLINEARITIES
	2.2 STABILIZATION OF MULTIDIMENSIONAL SOLITONS BY LINEAR OR NONLINEAR POTENTIALS
	2.3 THE GROSS–PITAEVSKII (GP) EQUATIONS WITH LEE–HUANG–YANG (LHY) CORRECTIONS FOR QUANTUM DROPLETS (QDs)
	2.4 TWO-COMPONENT SYSTEMS WITH SPIN–ORBIT COUPLING (SOC)
	REFERENCES
Chapter 3: The Use of Higher-Order Nonlinearities: Theory
	3.1 THE SHAPE AND STABILITY OF 2D FUNDAMENTAL SOLITONS SUPPORTED BY THE COMPETING CUBIC–QUINTIC (CQ) NONLINEAR TERMS
	3.2 STABILITY OF 2D VORTEX SOLITONS UNDER THE ACTION OF COMPETING NONLINEARITIES
	3.3 STABLE 3D SOLITONS WITH EMBEDDED VORTICITY S =1
	3.4 STABLE 2D AND 3D VORTEX SOLITONS IN SYSTEMS OF COUPLED EQUATIONS
	3.5 SPATIOTEMPORAL OPTICAL VORTICES (STOVs) AND SPONTANEOUS SYMMETRY BREAKING (SSB) IN A DUAL-CORE PLANAR WAVEGUIDE
	3.6 THE EFFECTIVE POTENTIAL OF AN INTERACTION BETWEEN FAR SEPARATED 2D AND 3D SOLITONS
	REFERENCES
Chapter 4: The Use of Higher-Order Nonlinearities: Experiments in Optical Media
	4.1 FUNDAMENTAL (2+1)D SOLITONS
	4.2 QUASI-STABLE (2+1)D VORTEX SOLITONS
	4.3 QUASI-STABLE ANNULAR SOLITON CLUSTERS (NECKLACE PATTERNS)
	4.4 ROTATING “PROPELLER” PATTERNS
	REFERENCES
Chapter 5: Linear Trapping Potentials
	5.1 STABILIZATION OF 3D AND 2D FUNDAMENTAL SOLITONS AND VORTICES BY THE TRAPPING POTENTIAL
	5.2 STABLE 2D TWO-COMPONENT SOLITONS WITH HIDDEN VORTICITY
	5.3 TRAPPING TWO-COMPONENT SOLITONS AND VORTICES IN A SET OF CONFINING AND EXPULSIVE POTENTIALS BY MEANS OF LINEAR COUPLING
	REFERENCES
Chapter 6: Nonlinear Trapping Potentials and Nonlinearity Management
	6.1 THE BASIC SETTING
	6.2 EXACT, APPROXIMATE, AND NUMERICAL RESULTS FOR THE ANTI-GAUSSIAN SPATIAL-MODULATION PROFILE
	6.3 GYROSCOPE SOLITONS (VORTEX TORI) IN 3D
	6.4 HOPFIONS: 3D SOLITONS WITH TWO INDEPENDENT TOPOLOGICAL CHARGES
	6.5 VORTEX–ANTIVORTEX HYBRIDS IN THE PEANUT-SHAPED MODULATION PROFILE
	6.6 LOCALIZED DARK VORTICES
	6.7 NONLINEARITY MANAGEMENT (NM)
	REFERENCES
Chapter 7: Spatially Periodic Potentials (Lattices): Theory
	7.1 BASIC EQUATIONS
	7.2 SOLITONS AND SOLITARY VORTICES STABILIZED BY THE LATTICE POTENTIAL
	7.3 2D COMPOUND STATES IN THE FORM OF HIGHER-ORDER VORTICES AND SUPERVORTICES
	7.4 TWO-DIMENSIONAL GAP SOLITONS (GSs) AND GAP VORTICES
	7.5 2D SOLITONS IN A RADIAL POTENTIAL
	7.6 GAP SOLITONS IN A 2D QUASI-PERIODIC LATTICE POTENTIAL (PENROSE TILING)
	7.7 STABILIZATION OF VORTICES IN THE SECOND-HARMONICGENERATING MEDIUM BY A LATTICE POTENTIAL
	REFERENCES
Chapter 8: Spatially Periodic Potentials (Lattices): Experiments
	8.1 2D VORTEX SOLITONS STABILIZED BY VIRTUAL PHOTONIC LATTICES IN PHOTOREFRACTIVE (PhR) MEDIA
	8.2 SPATIAL SOLITONS AND SPATIOTEMPORAL LIGHT BULLETS (LBs) IN MULTI-CORE BULK WAVEGUIDES
	REFERENCES
Chapter 9: Stabilization of Multidimensional Solitons by Spin–Orbit Coupling (SOC)
	9.1 INTRODUCTION TO THE TOPIC: INTERPLAY OF THE SOC AND NONLINEARITY
	9.2 THE TWO-COMPONENT SOC MODEL
	9.3 2D SOLITONS WITH THE RASHBA COUPLING
	9.4 EFFECT OF COMBINED RASHBA AND DRESSELHAUS SPIN–ORBIT COUPLINGS ON THE SV AND MM SOLITONS IN 2D
	9.5 2D SOLITONS UNDER THE ACTION OF THE ZEEMAN SPLITTING (ZS)
	9.6 SV GAP SOLITONS IN THE DIFFRACTIONLESS LIMIT
	9.7 METASTABLE 3D SOLITONS IN THE SOC SYSTEM
	REFERENCES
Chapter 10: Emulation of the Spin—Orbit Coupling (SOC) in Optical Systems
	10.1 SPATIOTEMPORAL SOLITONS IN DISPERSIVE DUAL-CORE COUPLERS
	10.2 SPATIOTEMPORAL SOLITONS IN THE SOC-EMULATING (PARITY-TIME)-SYMMETRIC DUAL-CORE COUPLER
	REFERENCES
Chapter 11: Quantum Droplets (QDs): Theory
	11.1 THEORETICAL MODELS OF QDS IN THREE, TWO, AND ONE DIMENSIONS
	11.2 STABLE QDs WITH EMBEDDED VORTICITY
	11.3 TWO-DIMENSIONAL VORTEX MODES TRAPPED IN A SINGULAR POTENTIAL
	REFERENCES
Chapter 12: Experiments: Quantum Droplets (QDs) in the BEC with Contact and Dipole–Dipole Interactions (DDIs)
	12.1 OBLATE (QUASI-2D ALIAS “PANCAKE-SHAPED”) DROPLETS
	12.2 THREE-DIMENSIONAL (ISOTROPIC) DROPLETS
	12.3 COLLISIONS BETWEEN ISOTROPIC QDs
	12.4 DROPLETS IN A HETERONUCLEAR BOSONIC MIXTURE
	12.5 DROPLETS IN THE DIPOLAR CONDENSATE OF DYSPROSIUM
	12.6 DROPLETS IN THE DIPOLAR CONDENSATE OF ERBIUM
	REFERENCES
Chapter 13: Multidimensional Solitons in Nonlocal Media
	13.1 INTRODUCTION TO THE TOPIC
	13.2 ANISOTROPIC QUASI-2D SOLITONS BUILT BY DIPOLE–DIPOLE INTERACTIONS (DDIs) IN BOSE–EINSTEIN CONDENSATE OF MAGNETIC ATOMS
	13.3 GIANT VORTEX RINGS (VRs) IN MICROWAVE-COUPLED BINARY BEC
	REFERENCES
Chapter 14: Multidimensional Dissipative Solitons and Solitary Vortices
	14.1 SPIRAL SOLITONS (VORTEX RINGS) PRODUCED BY THE 2D COMPLEX GINZBURG–LANDAU (CGL) EQUATION WITH THE CUBIC–QUINTIC (CQ) NONLIN
	14.2 DISSIPATIVE VORTEX SOLITONS STABILIZED BY THE FREQUENCY-SELECTIVE FEEDBACK
	14.3 WEAKLY LOCALIZED MODES IN MEDIA WITH NONLINEAR LOSSES (MULTI-PHOTON ABSORPTION)
	14.4 LOCALIZED STATES IN 2D NONLINEAR DISSIPATIVE MEDIA WITH SPATIALLY MODULATED GAIN OR LOSS
	14.5 TWO-DIMENSIONAL DSs (DISSIPATIVE SOLITONS) IN THE HO (HARMONIC-OSCILLATOR) TRAPPING POTENTIAL
	14.6 DISSIPATIVE VORTEX SOLITONS STABILIZED BY SPATIALLY PERIODIC (LATTICE) POTENTIALS
	14.7 TWO-COMPONENT DISSIPATIVE SOLITONS OF THE VORTEX–ANTIVORTEX (VAV) TYPE STABILIZED BY SOC (SPIN–ORBIT COUPLING)
	14.8 THREE-DIMENSIONAL DISSIPATIVE SOLITONS
	REFERENCES
Chapter 15: Conclusion
	REFERENCES
Index