scholarly journals Asymptotic behavior of the coupled Klein–Gordon–Schrödinger systems on compact manifolds

2021 ◽  
Author(s):  
César A. Bortot ◽  
Thales M. Souza ◽  
Janaina P. Zanchetta
Keyword(s):  
Asymptotic Behavior ◽  
Compact Manifolds ◽  
Klein Gordon ◽  
Schrödinger Systems

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

scholarly journals Decay of solutions of a system of nonlinear Klein-Gordon equations

1986 ◽  
Vol 9 (3) ◽  
pp. 471-483 ◽  
Author(s):  
José Ferreira ◽  
Gustavo Perla Menzala
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Finite Energy ◽  
Energy Norm ◽  
Local Energy ◽  
Decay Of Solutions ◽  
Klein Gordon

We study the asymptotic behavior in time of the solutions of a system of nonlinear Klein-Gordon equations. We have two basic results: First, in theL∞(ℝ3)norm, solutions decay like0(t−3/2)ast→+∞provided the initial data are sufficiently small. Finally we prove that finite energy solutions of such a system decay in local energy norm ast→+∞.

Sign in / Sign up

Export Citation Format

Share Document