scholarly journals High-momenta estimates for the Klein−Gordon equation: long-range magnetic potentials and time-dependent inverse scattering

2016 ◽  
Vol 49 (15) ◽  
pp. 155302 ◽  
Author(s):  
Miguel Ballesteros ◽  
Ricardo Weder
Keyword(s):  
Long Range ◽  
Inverse Scattering ◽  
Gordon Equation ◽  
Time Dependent ◽  
Klein Gordon ◽  
Magnetic Potentials ◽  
Klein Gordon Equation

scholarly journals A REMARK ON LONG RANGE SCATTERING FOR THE NONLINEAR KLEIN–GORDON EQUATION

2005 ◽  
Vol 02 (01) ◽  
pp. 77-89 ◽  
Author(s):  
HANS LINDBLAD ◽  
AVY SOFFER
Keyword(s):  
Asymptotic Expansion ◽  
Initial Data ◽  
Long Range ◽  
Gordon Equation ◽  
Scattering Problem ◽  
One Dimension ◽  
Complete Asymptotic Expansion ◽  
Arbitrary Size ◽  
Klein Gordon ◽  
Klein Gordon Equation

We consider the scattering problem for the nonlinear Klein–Gordon Equation with long range nonlinearity in one dimension. We prove that for all prescribed asymptotic solutions there is a solution of the equation with such behavior, for some choice of initial data. In the case the nonlinearity has the good sign (repulsive) the result hold for arbitrary size asymptotic data. The method of proof is based on reducing the long range phase effects to an ODE; this is done via an appropriate ansatz. We also find the complete asymptotic expansion of the solutions.

scholarly journals On morawetz estimates with time-dependent weights for the Klein-Gordon equation

2020 ◽  
Vol 40 (11) ◽  
pp. 6275-6288
Author(s):  
Jungkwon Kim ◽  
◽  
Hyeongjin Lee ◽  
Ihyeok Seo ◽  
Jihyeon Seok
Keyword(s):  
Gordon Equation ◽  
Time Dependent ◽  
Klein Gordon ◽  
Klein Gordon Equation

Asymptotic numerical solver for the linear Klein–Gordon equation with space- and time-dependent mass

2021 ◽  
Vol 115 ◽  
pp. 106935
Author(s):  
Marissa Condon ◽  
Karolina Kropielnicka ◽  
Karolina Lademann ◽  
Rafał Perczyński
Keyword(s):  
Gordon Equation ◽  
Time Dependent ◽  
Space And Time ◽  
Klein Gordon ◽  
Numerical Solver ◽  
Dependent Mass ◽  
Klein Gordon Equation

scholarly journals Linear stability of Mandal–Sengupta–Wadia black holes

2019 ◽  
Vol 34 (12) ◽  
pp. 1950094
Author(s):  
H. Gürsel ◽  
G. Tokgöz ◽  
İ. Sakallı
Keyword(s):  
Black Holes ◽  
Linear Stability ◽  
Gordon Equation ◽  
Small Time ◽  
Einstein Equations ◽  
Time Dependent ◽  
Small Perturbations ◽  
Klein Gordon ◽  
Dimensional Gravity ◽  
Klein Gordon Equation

In this paper, the linear stability of static Mandal–Sengupta–Wadia (MSW) black holes in (2 + 1)-dimensional gravity against circularly symmetric perturbations is studied. Our analysis only applies to non-extremal configurations, thus leaving out the case of the extremal (2 + 1) MSW solution. The associated fields are assumed to have small perturbations in these static backgrounds. We then consider the dilaton equation and specific components of the linearized Einstein equations. The resulting effective Klein–Gordon equation is reduced to the Schrödinger-like wave equation with the associated effective potential. Finally, it is shown that MSW black holes are stable against the small time-dependent perturbations.

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