Interacting Localized Solutions of the Nonlinear Klein—Gordon Equation with a Variable Mass

JETP Letters ◽  
2020 ◽  
Vol 111 (3) ◽  
pp. 193-195
Author(s):  
R. K. Salimov ◽  
E. G. Ekomasov
Keyword(s):  
Gordon Equation ◽  
Variable Mass ◽  
Localized Solutions ◽  
Klein Gordon ◽  
Klein Gordon Equation

scholarly journals Sharp comparison theorems for the Klein–Gordon equation in d dimensions

2016 ◽  
Vol 25 (06) ◽  
pp. 1650039 ◽  
Author(s):  
Richard L. Hall ◽  
Petr Zorin
Keyword(s):  
Gordon Equation ◽  
Scalar Potential ◽  
Variable Mass ◽  
Comparison Theorems ◽  
Time Component ◽  
Klein Gordon ◽  
Klein Gordon Equation

We establish sharp (or ’refined’) comparison theorems for the Klein–Gordon equation. We show that the condition [Formula: see text], which leads to [Formula: see text], can be replaced by the weaker assumption [Formula: see text] which still implies the spectral ordering [Formula: see text]. In the simplest case, for [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text] and for [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. We also consider sharp comparison theorems in the presence of a scalar potential [Formula: see text] (a ‘variable mass’) in addition to the vector term [Formula: see text] (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.

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
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