Decay and Asymptotics for the One-Dimensional Klein--Gordon Equation with Variable Coefficient Cubic Nonlinearities

DOI10.1137/20M1323722zbMath1455.35021arXiv1907.09922MaRDI QIDQ5141945

Jonas Lührmann, Hans Lindblad, Avy Soffer

Publication date: 29 December 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.09922

zbMATH Keywords

long-range scatteringasymptotic stability of kink solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Soliton equations (35Q51) Initial value problems for second-order hyperbolic equations (35L15) Ginzburg-Landau equations (35Q56) Second-order semilinear hyperbolic equations (35L71)

Related Items (20)

Linear and orbital stability analysis for solitary-wave solutions of variable-coefficient scalar-field equations ⋮ On asymptotic behavior of solutions to cubic nonlinear Klein-Gordon systems in one space dimension ⋮ Quadratic Klein-Gordon equations with a potential in one dimension ⋮ The 1-dimensional nonlinear Schrödinger equation with a weighted \(L^1\) potential ⋮ Nonexistence of global solutions to Klein-Gordon equations with variable coefficients power-type nonlinearities ⋮ Improved uniform error bounds of exponential wave integrator method for long-time dynamics of the space fractional Klein-Gordon equation with weak nonlinearity ⋮ Asymptotics and scattering for wave Klein-Gordon systems ⋮ Deterministic dynamics and randomness in PDE. Abstracts from the workshop held May 22--28, 2022 ⋮ Nonlinear waves and dispersive equations. Abstracts from the workshop held June 26 -- July 2, 2022 ⋮ Small energy stabilization for 1D nonlinear Klein Gordon equations ⋮ Asymptotic stability of the sine-Gordon kink under odd perturbations ⋮ On the \(1d\) cubic NLS with a non-generic potential ⋮ On the solution behavior of a nonlinear time-fractional Klein-Gordon equation: theoretical study and numerical validation ⋮ The matrix nonlinear Schrödinger equation with a potential ⋮ Einstein-Klein-Gordon spacetimes in the harmonic near-Minkowski regime ⋮ 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 ⋮ Asymptotic stability of kink with internal modes under odd perturbation ⋮ On selection of standing wave at small energy in the 1D cubic Schrödinger equation with a trapping potential ⋮ Soliton dynamics for the 1D quadratic Klein-Gordon equation with symmetry

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