Scattering operator for the fourth order nonlinear Schrödinger equation

DOI10.14492/hokmj/2018-907zbMath1479.35792OpenAlexW3188191812MaRDI QIDQ1982560

Pavel I. Naumkin, Yuichiro Kawahara, Nakao Hayashi

Publication date: 14 September 2021

Published in: Hokkaido Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.14492/hokmj/2018-907

zbMATH Keywords

scattering problemfourth order nonlinear Schrödinger equationnon gauge invariant

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quantum scattering theory (81U99) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (1)

Well‐posedness of generalized KdV and one‐dimensional fourth‐order derivative nonlinear Schrödinger equations for data with an infinite L² norm

Cites Work

• 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 \(d\geqslant 9\)
• Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case
• 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
• Well-posedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation
• Nonlinear scattering theory at low energy
• Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• 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 small solutions for the fourth-order nonlinear Schrödinger equation
• Scattering of solutions to the fourth-order nonlinear Schrödinger equation
• Scattering theory for the fourth-order Schrödinger equation in low dimensions
• Fourier Analysis and Nonlinear Partial Differential Equations
• THE MASS-CRITICAL FOURTH-ORDER SCHRÖDINGER EQUATION IN HIGH DIMENSIONS
• Self-Focusing with Fourth-Order Dispersion
• On the inhomogeneous fourth-order nonlinear Schrödinger equation
• 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
• Properties of nonlinear Schrodinger equations associated with diffeomorphism group representations
• On the Semirelativistic Hartree‐Type Equation

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