A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere

1994 ◽  
Vol 12 (2) ◽  
pp. 220 ◽  
Author(s):  
T. R. Robinson
Keyword(s):  
Boundary Value Problems ◽  
Gordon Equation ◽  
Boundary Value ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation

2020 ◽  
Author(s):  
Bayegizova Aigulim ◽  
Dadayeva Assiyat
Keyword(s):  
Boundary Value Problems ◽  
Integral Equations ◽  
Gordon Equation ◽  
Boundary Integral Equations ◽  
Boundary Value ◽  
Generalized Functions ◽  
Boundary Integral ◽  
Stationary Boundary ◽  
Klein Gordon ◽  
Klein Gordon Equation

The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.

scholarly journals Feynman propagators on static spacetimes

2018 ◽  
Vol 30 (03) ◽  
pp. 1850006 ◽  
Author(s):  
Jan Dereziński ◽  
Daniel Siemssen
Keyword(s):  
Gordon Equation ◽  
Boundary Value ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Electromagnetic Potential ◽  
Limiting Absorption Principle ◽  
Feynman Propagator ◽  
Klein Gordon ◽  
Klein Gordon Equation

We consider the Klein–Gordon equation on a static spacetime and minimally coupled to a static electromagnetic potential. We show that it is essentially self-adjoint on [Formula: see text]. We discuss various distinguished inverses and bisolutions of the Klein–Gordon operator, focusing on the so-called Feynman propagator. We show that the Feynman propagator can be considered the boundary value of the resolvent of the Klein–Gordon operator, in the spirit of the limiting absorption principle known from the theory of Schrödinger operators. We also show that the Feynman propagator is the limit of the inverse of the Wick rotated Klein–Gordon operator.

A note on the Klein-Gordon equation and its solutions with applications to certain boundary value problems involving waves in plasma and in the atmosphere

1994 ◽  
Vol 12 (2/3) ◽  
pp. 220-225 ◽  
Author(s):  
T. R. Robinson
Keyword(s):  
Cold Plasma ◽  
Infinite Order ◽  
Bessel Functions ◽  
Gordon Equation ◽  
Boundary Value ◽  
Homogeneous Equation ◽  
Klein Gordon ◽  
Delta Functions ◽  
Algebraic Solutions ◽  
Klein Gordon Equation

Abstract. Certain algebraic solutions of the Klein-Gordon equation which involve Bessel functions are examined. It is demonstrated that these functions constitute an infinite series, each term of which is the solution of a boundary value problem involving a combination of source functions which comprise delta functions and their derivatives to infinite order. In addition, solutions to the homogeneous equation are constructed which comprise a continuous spectrum over non-integer order. These solutions are discussed in the context of wave propagation in isotropic cold plasma and the atmosphere.

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