Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case

DOI10.1016/j.jde.2016.07.026zbMath1353.35262OpenAlexW2508102418MaRDI QIDQ738723

Jesus A. Mendez-Navarro, Pavel I. Naumkin, Nakao Hayashi

Publication date: 5 September 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.07.026

zbMATH Keywords

large time asymptoticsfourth-order nonlinear Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (13)

Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion ⋮ Asymptotics for the fractional nonlinear Schrödinger equation with \(2<\alpha <\frac{5}{2}\) ⋮ Asymptotics for the fourth-order nonlinear Schrödinger equation in 2D ⋮ High-speed transmission in long-haul electrical systems ⋮ Asymptotics for the modified Whitham equation ⋮ Global existence of small solutions for the fourth-order nonlinear Schrödinger equation ⋮ Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L² norm ⋮ Higher-order derivative nonlinear Schrödinger equation in the critical case ⋮ Asymptotics for the third-order nonlinear Schrödinger equation in the critical case ⋮ Scattering operator for the fourth order nonlinear Schrödinger equation ⋮ Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions ⋮ Dissipative character of asymptotics for the nonlinear fractional Schrödinger equation ⋮ Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear fourth-order Schrödinger equations with radial data
• Global existence and asymptotic behavior of the Cauchy problem for fourth-order Schrödinger equations with combined power-type nonlinearities
• Large time asymptotics for the fourth-order nonlinear Schrödinger equation
• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions \(d\geqslant 9\)
• The focusing energy-critical fourth-order Schrödinger equation with radial data
• Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces
• Asymptotics of solutions of the fourth order Schrödinger type equation with a dissipative nonlinearity
• Factorization technique for the fourth-order nonlinear Schrödinger equation
• Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case
• Remarks on NLS with higher order anisotropic dispersion
• Energy critical fourth-order Schrödinger equations with subcritical perturbations
• Limiting profile of the blow-up solutions for the fourth-order nonlinear Schrödinger equation
• The cubic fourth-order Schrödinger equation
• Global well-posedness and scattering for the focusing energy-critical nonlinear Schrödinger equations of fourth order in the radial case
• Well-posedness for the fourth-order nonlinear Schrödinger-type equation related to the vortex filament.
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• Well-posedness of initial value problem for fourth order nonlinear Schrödinger equation
• Global existence and asymptotic behavior of solutions to the fourth-order nonlinear Schrödinger equation in the critical case
• 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
• Wellposedness for the fourth order nonlinear Schrödinger equations
• Global well-posedness of the Cauchy problem for nonlinear Schrödinger-type equations
• Scattering of solutions to the fourth-order nonlinear Schrödinger equation
• Scattering theory for the fourth-order Schrödinger equation in low dimensions
• GLOBAL WELL-POSEDNESS FOR THE GENERALISED FOURTH-ORDER SCHRÖDINGER EQUATION
• Singular solutions of theL²-supercritical biharmonic nonlinear Schrödinger equation
• Ring-type singular solutions of the biharmonic nonlinear Schrödinger equation
• THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS
• Self-Focusing with Fourth-Order Dispersion
• On the inhomogeneous fourth-order nonlinear Schrödinger equation
• Modified wave operators for the fourth-order non-linear Schrödinger-type equation with cubic non-linearity
• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Note on a modification to the nonlinear Schrödinger equation for application to deep water waves
• Motion and expansion of a viscous vortex ring. Part 1. A higher-order asymptotic formula for the velocity
• Remark on well-posedness for the fourth order nonlinear Schrödinger type equation
• Dispersion estimates for fourth order Schrödinger equations
• A Refined Well-Posedness for the Fourth-Order Nonlinear Schrödinger Equation Related to the Vortex Filament

This page was built for publication: Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case