Classical theory of Klein–Gordon equations with logarithmic nonlinearities

1978 ◽  
Vol 56 (11) ◽  
pp. 1405-1411 ◽  
Author(s):  
T. F. Morris
Keyword(s):  
Classical Theory ◽  
Nonlinear Interaction ◽  
Finite Energy ◽  
Positive Functional ◽  
Soliton Theory ◽  
All Solutions ◽  
Klein Gordon ◽  
Nonzero Charge

The relativistic soliton theory of Bialynicki-Birula and Mycielski is reviewed, and extended by the addition of a term in [Formula: see text] to the nonlinear interaction. For suitable values of the coupling, the energy becomes a positive functional which can be treated by a variational method.Evidence is presented which suggests that all solutions with finite energy and nonzero charge are localized.

Electrodynamics of charged scalar solitons

1979 ◽  
Vol 57 (12) ◽  
pp. 2171-2177 ◽  
Author(s):  
T. F. Morris
Keyword(s):  
Hamiltonian Formalism ◽  
Finite Energy ◽  
The Self ◽  
Equivalent Problem ◽  
Complex Scalar ◽  
Charged Scalar ◽  
Localized Solutions ◽  
Interaction Solutions ◽  
Complex Scalar Field ◽  
Nonzero Charge

The electrodynamics of a nonlinear, complex scalar field is developed from the basis of a Hamiltonian formalism. By means of a canonical transformation, the equations for a stationary state are reduced to the consideration of an equivalent problem in static equilibrium. Localized solutions are defined. For specified conditions on the self-interaction, solutions of finite energy, and finite, nonzero charge, are localized.

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→+∞.

Classification of U(1)-vortices with target ℂN

2015 ◽  
Vol 26 (13) ◽  
pp. 1550109 ◽  
Author(s):  
Guangbo Xu
Keyword(s):  
Complex Plane ◽  
Moduli Spaces ◽  
Finite Energy ◽  
Adiabatic Limit ◽  
Target Space ◽  
Vortex Equation ◽  
All Solutions

We study the symplectic vortex equation over the complex plane, for the target space [Formula: see text] ([Formula: see text]) with diagonal [Formula: see text]-action. Using adiabatic limit argument, we classify all solutions with finite energy and identify their moduli spaces, which generalizes Taubes’ result for [Formula: see text].

scholarly journals Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric

2021 ◽  
Vol 18 (02) ◽  
pp. 293-310
Author(s):  
Nicolas Besset ◽  
Dietrich Häfner
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
Half Plane ◽  
Gordon Equation ◽  
Finite Energy ◽  
De Sitter ◽  
Klein Gordon ◽  
Upper Half Plane ◽  
Small Charge ◽  
Klein Gordon Equation

We show the existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the De Sitter–Kerr–Newman metric for small charge and mass of the field and small angular momentum of the black hole. The mechanism behind is that the zero resonance that exists for zero charge, mass and angular momentum moves into the upper half plane.

On the coupled time-harmonic motion of a freely floating body and water covered by brash ice

2016 ◽  
Vol 795 ◽  
pp. 174-186 ◽  
Author(s):  
Nikolay Kuznetsov ◽  
Oleg Motygin
Keyword(s):  
Small Amplitude ◽  
Finite Interval ◽  
Finite Energy ◽  
Floating Body ◽  
Coupled Motion ◽  
Time Harmonic ◽  
All Solutions ◽  
Equipartition Of Energy ◽  
Linear Setting ◽  
Inverse Procedure

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

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