Scattering of solutions to the fourth-order nonlinear Schrödinger equation

DOI10.1142/S0219199715500352zbMath1345.35101OpenAlexW2077756600MaRDI QIDQ2800058

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

Publication date: 14 April 2016

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199715500352

zbMATH Keywords

large time asymptoticsfourth-order nonlinear Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51)

Related Items (9)

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 fourth-order nonlinear Schrödinger 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 ⋮ On the inhomogeneous biharmonic nonlinear Schrödinger equation: local, global and stability results ⋮ Scattering operator for the fourth order nonlinear Schrödinger equation ⋮ Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case ⋮ Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

Cites Work

• Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions \(d\geqslant 9\)
• Asymptotics of solutions of the fourth order Schrödinger type equation with a dissipative nonlinearity
• 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.
• Global existence of solutions for a fourth-order nonlinear Schrödinger equation
• Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
• THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
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