Global existence of small solutions for the fourth-order nonlinear Schrödinger equation

DOI10.1007/s00030-016-0420-zzbMath1367.35148OpenAlexW2549712534MaRDI QIDQ2397180

Kazuki Aoki, Pavel I. Naumkin, Nakao Hayashi

Publication date: 29 May 2017

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-016-0420-z

zbMATH Keywords

global existencefourth-order nonlinear Schrödinger equationnon gauge invariant

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (8)

Regularity properties of the cubic biharmonic Schrödinger equation on the half line ⋮ Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion ⋮ Asymptotics for the fourth-order nonlinear Schrödinger equation in 2D ⋮ On the inhomogeneous biharmonic nonlinear Schrödinger equation: local, global and stability results ⋮ Global existence of small solutions for a quadratic nonlinear fourth-order Schrödinger equation in six space dimensions ⋮ Scattering operator for the fourth order nonlinear Schrödinger equation ⋮ The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line ⋮ Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

Cites Work

• On the new critical exponent for the nonlinear Schrödinger equations
• Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case
• Domain and range of the modified wave operator for Schrödinger equations with a critical nonlinearity
• Nonlinear scattering theory at low energy
• Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament.
• Well-posedness for the fourth-order nonlinear derivative Schrödinger equation in higher dimension
• Global existence of solutions for a fourth-order nonlinear Schrödinger equation
• The Cauchy problem for the fourth-order nonlinear Schrödinger equation related to the vortex filament
• Scattering of solutions to the fourth-order nonlinear Schrödinger equation
• GLOBAL WELL-POSEDNESS FOR THE GENERALISED FOURTH-ORDER SCHRÖDINGER EQUATION
• Global existence of small solutions to quadratic nonlinear schrödinger equations
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Dispersion estimates for fourth order Schrödinger equations

This page was built for publication: Global existence of small solutions for the fourth-order nonlinear Schrödinger equation