Dynamics near the threshold for blowup in the one-dimensional focusing nonlinear Klein-Gordon equation

DOI10.1063/1.3645363zbMath1272.35174arXiv1012.1033OpenAlexW1978343920MaRDI QIDQ2851721

Piotr Bizoń, Tadeusz Chmaj, N. Szpak

Publication date: 2 October 2013

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

Full work available at URL: https://arxiv.org/abs/1012.1033

Mathematics Subject Classification ID

Model quantum field theories (81T10) NLS equations (nonlinear Schrödinger equations) (35Q55) Blow-up in context of PDEs (35B44)

Related Items (15)

Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes ⋮ Blow-up behavior for the Klein-Gordon and other perturbed semilinear wave equations ⋮ On asymptotic stability of the sine-Gordon kink in the energy space ⋮ Asymptotic stability of the sine-Gordon kink under odd perturbations ⋮ Asymptotic stability near the soliton for quartic Klein-Gordon equation in 1D ⋮ Convergence Analysis for a Three-Level Finite Difference Scheme of a Second Order Nonlinear ODE Blow-Up Problem ⋮ Stable blowup for the cubic wave equation in higher dimensions ⋮ Oscillons in the presence of external potential ⋮ Boundary scattering in the \(\phi^4\) model ⋮ On the stability of the notion of non-characteristic point and blow-up profile for semilinear wave equations ⋮ A sufficient condition for asymptotic stability of kinks in general (1+1)-scalar field models ⋮ Solution to the semilinear wave equation with a pyramid-shaped blow-up surface ⋮ On asymptotic stability of nonlinear waves ⋮ On similarity in the evolution of semilinear wave and Klein-Gordon equations: Numerical surveys ⋮ Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Global dynamics above the ground state energy for the focusing nonlinear Klein-Gordon equation
• Uniform estimates for solutions of nonlinear Klein-Gordon equations
• Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations
• Saddle points and instability of nonlinear hyperbolic equations
• Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension
• Numerical study of the blowup/global existence dichotomy for the focusing cubic nonlinear Klein–Gordon equation
• Saddle-point dynamics of a Yang–Mills field on the exterior Schwarzschild spacetime

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