On a Generalized Wave Equation and its Application

2020 ◽  
Vol 86 (1) ◽  
pp. 129-138
Author(s):  
Do-Hyung Kim
Keyword(s):  
Wave Equation ◽  
Generalized Wave Equation

On the solution of homogeneous generalized wave equation

1992 ◽  
Vol 33 (11) ◽  
pp. 3757-3758 ◽  
Author(s):  
E. Capelas de Oliveira
Keyword(s):  
Wave Equation ◽  
Generalized Wave Equation

Octonic massless field equations

2015 ◽  
Vol 30 (15) ◽  
pp. 1550084 ◽  
Author(s):  
Süleyman Demir ◽  
Murat Tanişli ◽  
Mustafa Emre Kansu
Keyword(s):  
Wave Equation ◽  
Field Equations ◽  
Real Component ◽  
Conservation Of Energy ◽  
Mathematical Structures ◽  
Massless Field ◽  
Energy Concept ◽  
Linear Gravity ◽  
Massless Fields ◽  
Generalized Wave Equation

In this paper, it is proven that the associative octons including scalar, pseudoscalar, pseudovector and vector values are convenient and capable tools to generalize the Maxwell–Dirac like field equations of electromagnetism and linear gravity in a compact and simple way. Although an attempt to describe the massless field equations of electromagnetism and linear gravity needs the sixteen real component mathematical structures, it is proved that these equations can be formulated in terms of eight components of octons. Furthermore, the generalized wave equation in terms of potentials is derived in the presence of electromagnetic and gravitational charges (masses). Finally, conservation of energy concept has also been investigated for massless fields.

DISSIPATIVE QUASI-PARTICLES: THE GENERALIZED WAVE EQUATION APPROACH

2002 ◽  
Vol 12 (11) ◽  
pp. 2435-2444 ◽  
Author(s):  
C. I. CHRISTOV
Keyword(s):  
Wave Equation ◽  
Difference Scheme ◽  
Energy Production ◽  
Wave Equations ◽  
Equation Approach ◽  
Quasi Particle ◽  
Localized Solutions ◽  
Long Time ◽  
Localized Waves ◽  
Generalized Wave Equation

Generalized Wave Equations containing dispersion, dissipation and energy-production (GDWE) are considered in lieu of dissipative NEE as more suitable models for two-way interaction of localized waves. The quasi-particle behavior and the long-time evolution of localized solutions upon take-over and head-on collisions are investigated numerically by means of an adequate difference scheme which represents faithfully the balance/conservation laws. It is shown that in most cases the balance between energy production/dissipation and nonlinearity plays a similar role to the classical Boussinesq balance between dispersion and nonlinearity, namely it can create and support localized solutions which behave as quasi-particles upon collisions and for a reasonably long time after that.

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