scholarly journals Unified discrete mechanics III: the hyperincursive discrete Klein-Gordon equation bifurcates to the 4 incursive discrete Majorana and Dirac equations and to the 16 Proca equations

2019 ◽  
Vol 1251 ◽  
pp. 012002 ◽  
Author(s):  
Daniel M Dubois
Keyword(s):  
Gordon Equation ◽  
Discrete Mechanics ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Proca Equations ◽  
Klein Gordon Equation

BILINEAR ESTIMATES AND APPLICATIONS TO GLOBAL WELL-POSEDNESS FOR THE DIRAC–KLEIN–GORDON EQUATION ON ℝ1+1

2013 ◽  
Vol 10 (01) ◽  
pp. 1-35 ◽  
Author(s):  
TIMOTHY CANDY
Keyword(s):  
Global Existence ◽  
Gordon Equation ◽  
Well Posedness ◽  
Bilinear Estimates ◽  
Dirac Equations ◽  
Klein Gordon ◽  
Nonlinear Dirac Equations ◽  
Klein Gordon Equation

We prove new bilinear estimates for the [Formula: see text] spaces which are optimal up to endpoints. These estimates are often used in the theory of nonlinear Dirac equations on ℝ1+1. As an application, by using the I-method of Colliander, Keel, Staffilani, Takaoka and Tao, we extend the work of Tesfahun on global existence below the charge class for the Dirac–Klein–Gordon equation on ℝ1+1.

scholarly journals Fractional Klein-Gordon equation with singular mass

2021 ◽  
Vol 143 ◽  
pp. 110579
Author(s):  
Arshyn Altybay ◽  
Michael Ruzhansky ◽  
Mohammed Elamine Sebih ◽  
Niyaz Tokmagambetov
Keyword(s):  
Gordon Equation ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

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