Quadratic nonlinear Klein-Gordon equation in one dimension

DOI10.1063/1.4759156zbMath1282.35347OpenAlexW2028770841MaRDI QIDQ2872296

Nakao Hayashi, Pavel I. Naumkin

Publication date: 14 January 2014

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

Full work available at URL: https://doi.org/10.1063/1.4759156

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Wave equation (35L05) NLS equations (nonlinear Schrödinger equations) (35Q55)

Related Items (15)

The nonlinear Schrödinger equation with a potential ⋮ A note on a system of cubic nonlinear Klein-Gordon equations in one space dimension ⋮ Quadratic Klein-Gordon equations with a potential in one dimension ⋮ Asymptotic stability of the sine-Gordon kink under odd perturbations ⋮ Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space ⋮ Decay and Asymptotics for the One-Dimensional Klein--Gordon Equation with Variable Coefficient Cubic Nonlinearities ⋮ Semiclassical microlocal normal forms and global solutions of modified one-dimensional KG equations ⋮ Absence of shocks for one dimensional Euler-Poisson system ⋮ Large time asymptotics for the fractional order cubic nonlinear Schrödinger equations ⋮ Global existence and asymptotics for quasi-linear one-dimensional Klein-Gordon equations with mildly decaying Cauchy data ⋮ A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models ⋮ Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities ⋮ On asymptotic stability of nonlinear waves ⋮ Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry ⋮ Dynamics of strongly interacting kink-antikink pairs for scalar fields on a line

Cites Work

• The initial value problem for the quadratic nonlinear Klein-Gordon equation
• The initial value problem for the cubic nonlinear Klein-Gordon equation
• The unit condition and global existence for a class of nonlinear Klein- Gordon equations
• On the asymptotic behavior of solutions of semi-linear wave equations
• On global small amplitude solutions to systems of cubic nonlinear Klein--Gordon equations with different mass terms in one space dimension
• Decay for nonlinear Klein-Gordon equations
• Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions
• Existence globale et comportement asymptotique pour l'équation de Klein–Gordon quasi linéaire à données petites en dimension 1
• Final state problem for the cubic nonlinear Klein–Gordon equation
• SCATTERING OPERATOR FOR NONLINEAR KLEIN–GORDON EQUATIONS
• 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
• Weighted Sobolev spaces applied to nonlinear Klein-Gordon equation

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