Existence and stability of standing waves for nonlinear fractional Schrödinger equations

DOI10.1063/1.4746806zbMath1278.35229OpenAlexW2013153702MaRDI QIDQ2872226

Daiwen Huang, Bo-ling Guo

Publication date: 14 January 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4746806

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for second-order parabolic equations (35K15) Fractional partial differential equations (35R11)

Related Items

On fractional Schrödinger systems of Choquard type, Lie-Trotter operator splitting spectral method for linear semiclassical fractional Schrödinger equation, Soliton dynamics in a fractional complex Ginzburg-Landau model, Stabilization of single- and multi-peak solitons in the fractional nonlinear Schrödinger equation with a trapping potential, Stabilization of fundamental solitons in the nonlinear fractional Schrödinger equation with \(\text{PT}\)-symmetric nonlinear lattices, Propagation dynamics of abruptly autofocusing circular Airy Gaussian vortex beams in the fractional Schrödinger equation, Solutions of nonlinear Schrödinger equation with fractional Laplacian without the Ambrosetti-Rabinowitz condition, Weak solution of the equation for a fractional porous medium with a forcing term, Dynamics of the nonlinear Hartree equation with a focusing and defocusing perturbation, Fourth-order time-stepping compact finite difference method for multi-dimensional space-fractional coupled nonlinear Schrödinger equations, Mass concentration phenomenon for inhomogeneous fractional Hartree equations, Existence of the stable traveling wave for half-wave equation with L²-critical combined nonlinearities, Truncated-Bloch-wave solitons in nonlinear fractional periodic systems, Sharp threshold of blow-up and scattering for the fractional Hartree equation, Gap Solitons in Fractional Dimensions With a Quasi‐Periodic Lattice, Existence of stable standing waves for the fractional Schrödinger equations with combined nonlinearities, On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation, Existence and stability of traveling waves for semi-relativistic Schrödinger equations with van der Waals-type potentials, On coupled nonlinear Schrödinger systems, Orbital stability of standing waves of a class of fractional Schrödinger equations with Hartree-type nonlinearity, Ground state solutions for a class of nonlinear fractional Schrödinger-Poisson systems with super-quadratic nonlinearity, Monotonicity of standing waves for the generalized fractional Schrödinger equations, Anisotropic Gagliardo-Nirenberg inequality with fractional derivatives, A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations, Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities, Existence and stability of normalized solutions to the mixed dispersion nonlinear Schrödinger equations, On the orbital stability of fractional Schrödinger equations, The ground states for theNcoupled nonlinear fractional Schrödinger equations, Existence of ground state solutions for a class of nonlinear fractional Schrödinger–Poisson systems with super-quadratic nonlinearity, Ground state solution and nodal solution for fractional nonlinear Schrödinger equation with indefinite potential, Existence of stable standing waves for the fractional Schrödinger equations with combined power-type and Choquard-type nonlinearities, On the existence and stability of standing waves for 2-coupled nonlinear fractional Schrödinger system, Solitary wave solutions for nonlinear fractional Schrödinger equation in Gaussian nonlocal media, Existence and instability of normalized standing waves for the fractional Schrödinger equations in the L2-supercritical case, Nondegeneracy and stability of antiperiodic bound states for fractional nonlinear Schrödinger equations, Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schrödinger equation, Bound state for fractional Schrödinger equation with saturable nonlinearity, Lipschitz stability criteria for functional differential systems of fractional order, Remark on local solvability of the Cauchy problem for semirelativistic equations, Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type and power type nonlinearities, Global existence for the nonlinear fractional Schrödinger equation with fractional dissipation, Blow-up of solutions for semilinear fractional Schrödinger equations, Modulational instability in fractional nonlinear Schrödinger equation, On global existence for mass-supercritical nonlinear fractional Hartree equations, Asymptotic behavior of constraint minimizers for the mass-critical fractional nonlinear Schrödinger equation with a subcritical perturbation, Stability and instability of standing waves for the fractional nonlinear Schrödinger equations, Dynamics of solutions of a fractional NLS system with quadratic interaction, Radial sign-changing solution for fractional Schrödinger equation, Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential, Remarks on the inhomogeneous fractional nonlinear Schrödinger equation, Orbital stability of standing waves for fractional Hartree equation with unbounded potentials, Stable standing waves of nonlinear fractional Schrödinger equations, Normalized ground states for general pseudo-relativistic Schrödinger equations, Remarks on damped fractional Schrödinger equation with pure power nonlinearity, Soliton dynamics for fractional Schrödinger equations, Existence of solitary-wave solutions to nonlocal equations, Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity

Cites Work

• Unnamed Item
• Gauge invariance in fractional field theories
• Nonlinear scalar field equations. I: Existence of a ground state
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Semigroups of linear operators and applications to partial differential equations
• Existence of solitary waves in higher dimensions
• Fractional quantum mechanics and Lévy path integrals
• Existence of the global smooth solution to the period boundary value problem of fractional nonlinear Schrödinger equation
• Some physical applications of fractional Schrödinger equation
• Commutator estimates and the euler and navier-stokes equations
• Elliptic Partial Differential Equations of Second Order
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• The random walk's guide to anomalous diffusion: A fractional dynamics approach