Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities

Abstract

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons and discuss other applications of interest to the field of nonlinear matter waves.

References in corpus (20)

• Formation and Propagation of Matter Wave Soliton Trains
• Formation of a Matter-Wave Bright Soliton
• Dark Solitons in Bose-Einstein Condensates
• Dynamics of collapsing and exploding Bose-Einstein condensates
• Bright gap solitons of atoms with repulsive interaction
• Tuning the scattering length with an optically induced Feshbach resonance
• Formation of bright matter-wave solitons during the collapse of Bose-Einstein condensates
• Dynamically Stabilized Bright Solitons in a Two-Dimensional Bose-Einstein Condensate
• Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
• Adiabatic dynamics of periodic waves in Bose-Einstein condensate with time dependent atomic scattering length
• Controllable soliton emission from a Bose-Einstein condensate
• Matter-wave solitons of collisionally inhomogeneous condensates
• Stabilization of solitons of the multidimensional nonlinear Schrodinger equation: Matter-wave breathers
• Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length
• Feshbach resonance induced shock waves in Bose-Einstein condensates
• Transmission of matter wave solitons through nonlinear traps and barriers
• Analysis of an atom laser based on the spatial control of the scattering length
• Propagation of matter wave solitons in periodic and random nonlinear potentials
• Localized modes in arrays of boson-fermion mixtures
• Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Cited by in corpus (102)

• Solitons in nonlinear lattices
• Dark solitons in atomic Bose-Einstein condensates: from theory to experiments
• Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques
• Localized nonlinear waves in systems with time- and space-modulated nonlinearities
• Solitons in combined linear and nonlinear lattice potentials
• Nonautonomous "rogons" in the inhomogeneous nonlinear Schrodinger equation with variable coefficients
• Quantized Quasi-Two Dimensional Bose-Einstein Condensates with Spatially Modulated Nonlinearity
• Quantum dynamics with spatiotemporal control of interactions in a stable Bose-Einstein condensate
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Bright solitons from defocusing nonlinearities
• Spatiotemporal engineering of matter-wave solitons in Bose-Einstein condensates
• Exact solutions to three-dimensional generalized nonlinear Schrodinger equations with varying potential and nonlinearities
• Spatial solitons and stability in self-focusing and defocusing Kerr nonlinear media with generalized PT-symmetric Scarff-II potentials
• Algebraic bright and vortex solitons in defocusing media
• Stable two-dimensional solitons in nonlinear lattices
• Solitons in a nonlinear Schrodinger equation with PT-symmetric potentials and inhomogeneous nonlinearity: stability and excitation of nonlinear modes
• Quantized vortices in a rotating Bose-Einstein condensate with spatiotemporally modulated interaction
• Rogue Waves In Nonlinear Schrödinger Models with Variable Coefficients: Application to Bose-Einstein Condensates
• One-dimensional gap solitons in quintic and cubic-quintic Fractional nonlinear Schrödinger equations with a periodically modulated linear potential
• Soliton modes, stability, and drift in optical lattices with spatially modulated nonlinearity
• Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices
• Three-dimensional hybrid vortex solitons
• Solitons supported by localized nonlinearities in periodic media
• Matter-wave solitons with a periodic, piecewise-constant nonlinearity
• Vector solitons in nonlinear lattices
• Analytical three-dimensional bright solitons and soliton-pairs in Bose-Einstein condensates with time-space modulation
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Matter-wave solutions in the Bose-Einstein condensates with the harmonic and Gaussian potentials
• Solitons and their stability in the nonlocal nonlinear Schroedinger equation with PT-symmetric potentials
• Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices
• Power-dependent shaping of vortex solitons in optical lattices with spatially modulated nonlinear refractive index
• Soliton oscillations in collisionally inhomogeneous attractive Bose-Einstein condensates
• Light bullets in Bessel optical lattices with spatially modulated nonlinearity
• Stabilization of multi-beam necklace solitons in circular arrays with spatially modulated nonlinearity
• Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients
• Solitary waves in coupled nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities
• Photon-atomic solitons in a Bose-Einstein condensate trapped in a soft optical lattice
• Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices
• Supersolitons: Solitonic excitations in atomic soliton chains
• Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation
• Propagation of solitons in thermal media with periodic nonlinearity
• Dissipative Dynamics of Matter Wave Soliton in Nonlinear Optical Lattice
• Localization phenomena in Nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates
• Delocalizing transition in one-dimensional condensates in optical lattices due to inhomogeneous interactions
• Arrayed and checkerboard optical waveguides controlled by the electromagnetically-induced transparency
• Solitons supported by spatially inhomogeneous nonlinear losses
• Stabilization of two-dimensional solitons in cubic-saturable nonlinear lattices
• Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity
• Matter-wave 2D solitons in crossed linear and nonlinear optical lattices
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• Laser tweezers for atomic solitons
• Suppression of the critical collapse for one-dimensional solitons by saturable quintic nonlinear lattices
• Solitons supported by singular spatial modulation of the Kerr nonlinearity
• Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity
• Modulation of breathers in the three-dimensional nonlinear Gross-Pitaevskii equation
• Vector rogue waves and dark-bright boomeronic solitons in autonomous and non-autonomous settings
• Two-Dimensional Superfluid Flows in Inhomogeneous Bose-Einstein Condensates
• Quasi-one-dimensional Bose-Einstein condensates in nonlinear lattices
• Dust fluid component from Lie symmetries in Scalar field Cosmology
• Spatially modulated two- and three-component Rabi-coupled Gross-Pitaevskii systems
• On the inhomogeneous NLS with inverse-square potential
• Asymmetric solitons and domain walls supported by inhomogeneous defocusing nonlinearity
• Spontaneous symmetry breaking of photonic and matter waves in two-dimensional pseudopotentials
• Exact Bright and Dark Spatial Soliton Solutions in Saturable Nonlinear Media
• State transition induced by self-steepening and self phase-modulation
• Soliton dynamics at an interface between uniform medium and nonlinear optical lattice
• Collisional-inhomogeneity-induced generation of matter-wave dark solitons
• Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation
• Existence of dark solitons in a class of stationary nonlinear Schrödinger equations with periodically modulated nonlinearity and periodic asymptotic
• Wide Localized Solitons in Systems with Time and Space-Modulated Nonlinearities
• Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials
• Analytical solutions to the spin-1 Bose-Einstein condensates
• Asymmetric localized states in periodic potentials with a domain wall-like Kerr nonlinearity
• Exactly solvable Gross-Pitaevskii type equations
• Dark Solitary Waves in a Class of Collisionally Inhomogeneous Bose-Einstein Condensates
• Regular and chaotic Bose-Einstein condensate in an accelerated Wannier-Stark lattice
• Similarity Inner Solutions for the Pulsar Equation
• Transfer and scattering of wave packets by a nonlinear trap
• Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain
• Lie Symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities
• Averaging of Nonlinearity Management with Dissipation
• Two-dimensional vector solitons stabilized by a linear or nonlinear lattice acting in one component
• Noether symmetries and conservation laws of a reduced gauged bilayer graphene model
• Coupled density-spin Bose-Einstein condensates dynamics and collapse in systems with quintic nonlinearity
• Explicit solutions with non-trivial phase of the inhomogeneous coupled two-component NLS system
• Well-posedness and scattering of inhomogeneous cubic-quintic NLS
• Matter-Wave Solitons in the Presence of Collisional Inhomogeneities: Perturbation theory and the impact of derivative terms
• A novel exact solution to transmission problem of electron wave in a nonlinear Kronig-Penney superlattice
• Solitons in thermal media with periodic modulation of linear refractive index
• Riemann-Hilbert approach to the inhomogeneous fifth-order nonlinear Schrödinger equation with non-vanishing boundary conditions
• On the GWP of focusing energy-ciritical inhomogeneous NLS
• Exact solutions for periodic and solitary matter waves in nonlinear lattices
• Small data scattering of the inhomogeneous cubic-quintic NLS in 2 dimensions
• Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of EP Lie algebra
• On the focusing energy-critical inhomogeneous NLS: weighted space approach
• Lie symmetry classification for the 1+1 and 1+2 generalized Zoomeron equations
• NLS equation with competing inhomogeneous nonlinearities: ground states, blow-up, and scattering
• The Cauchy problem for the energy-critical inhomogeneous nonlinear Schrödinger equation with inverse-square potential
• Solitary waves and their linear stability in nonlinear lattices
• Scattering theory for 3d cubic inhomogeneous NLS with inverse square potential
• Localized Analytical Solutions and Parameters Analysis in the Nonlinear Dispersive Gross-Pitaevskii Mean-Field GP (m,n) Model with Space-Modulated Nonlinearity and Potential
• Solution of the Master Equation for Quantum Brownian Motion given by the Schrödinger Equation