On small traveling waves to the mass critical fractional NLS

DOI10.1007/s00526-018-1355-5zbMath1410.35210arXiv1712.04484OpenAlexW2771648509MaRDI QIDQ1650906

Pierre Raphaël, I. P. Naumkin

Publication date: 16 July 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.04484

zbMATH Keywords

existenceground statetraveling waveasymptotic profilefractional nonlinear Schrodinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Traveling wave solutions (35C07) Fractional partial differential equations (35R11)

Related Items (3)

Nondispersive solutions to the mass critical half-wave equation in two dimensions ⋮ Existence of the stable traveling wave for half-wave equation with L²-critical combined nonlinearities ⋮ Existence and stability of traveling waves for semi-relativistic Schrödinger equations with van der Waals-type potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniqueness of non-linear ground states for fractional Laplacians in \(\mathbb{R}\)
• Explicit formula for the solution of the Szegö equation on the real line and applications
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Global well-posedness, scattering and blow-up for the energy-critical, focusing, nonlinear Schrö\-dinger equation in the radial case
• Global well-posedness and scattering for the mass critical nonlinear Schrödinger equation with mass below the mass of the ground state
• Instability of vortex solitons for 2D focusing NLS
• Nondispersive solutions to the \(L ^{2}\)-critical half-wave equation
• Boson stars as solitary waves
• The cubic Szegő equation
• Two-soliton solutions to the three-dimensional gravitational Hartree equation
• Spectra of Linearized Operators for NLS Solitary Waves
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
• Remarks on the Blowup for the $L^2$‐Critical Nonlinear Schrödinger Equations

This page was built for publication: On small traveling waves to the mass critical fractional NLS