Final state problem for the cubic nonlinear Klein–Gordon equation

DOI10.1063/1.3215980zbMath1283.35056OpenAlexW2055765999MaRDI QIDQ3583650

Nakao Hayashi, Pavel I. Naumkin

Publication date: 17 August 2010

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3215980

zbMATH Keywords

Fourier transformsnonlinear differential equationsSchrödinger equationwave equationspartial differential equations

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Second-order semilinear hyperbolic equations (35L71)

Related Items (10)

Modified Wave Operator for a System of Nonlinear Schrödinger Equations in 2d ⋮ Modified scattering for the Klein-Gordon equation with the critical nonlinearity in three dimensions ⋮ The initial value problem for the quadratic nonlinear Klein-Gordon equation ⋮ A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension ⋮ Modified scattering for the quadratic nonlinear Klein–Gordon equation in two dimensions ⋮ Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions ⋮ Remarks on decay of small solutions to systems of Klein-Gordon equations with dissipative nonlinearities ⋮ Orbital stability of Dirac solitons ⋮ Critical nonlinear Schrödinger equations in higher space dimensions ⋮ Quadratic nonlinear Klein-Gordon equation in one dimension

Cites Work

• Unnamed Item
• On space-time means and everywhere defined scattering operators for nonlinear Klein-Gordon equations
• Nonlinear small data scattering for the wave and Klein-Gordon equation
• On scattering and everywhere defined scattering operators for nonlinear Klein-Gordon equations
• Low energy scttering for nonlinear Klein-Gordon equations
• Existence of solutions for Schrödinger evolution equations
• Nonlinear scattering theory at low energy
• Long range scattering for nonlinear Schrödinger equations in one space dimension
• Modified wave operators for the derivative nonlinear Schrödinger equation
• On global small amplitude solutions to systems of cubic nonlinear Klein--Gordon equations with different mass terms in one space dimension
• Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential
• Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions
• A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation
• Large time behavior of solutions to the Klein-Gordon equation with nonlinear dissipative terms
• Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
• Global existence of small amplitude solutions to nonlinear klein-gordon equations in four space-time dimensions
• Normal forms and quadratic nonlinear Klein-Gordon equations
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Decay estimates for the Klein ndesh Gordon equation
• The initial value problem for the derivative nonlinear Schrödinger equation in the energy space
• Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation
• A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION

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