Search results for "Inhomogeneous electromagnetic wave equation"

showing 5 items of 5 documents

On new ways of group methods for reduction of evolution-type equations

2005

AbstractNew exact solutions of the evolution-type equations are constructed by means of a non-point (contact) symmetries. Also we analyzed the discrete symmetries of Maxwell equations in vacuum and decoupled ones to the four independent equations that can be solved independently.

Exact solutionGroup (mathematics)Independent equationApplied MathematicsMathematical analysisInhomogeneous electromagnetic wave equationEuler equationsSymmetrysymbols.namesakereaction-diffusion equationsExact solutions in general relativityMaxwell's equationsSimultaneous equationsHomogeneous spacesymbolsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Symmetries and Covariance of the Maxwell Equations

2012

Already within a given, fixed division of four-dimensional spacetime into the space where experiments are performed, and the laboratory time variable, Maxwell’s equations show interesting transformation properties under continuous and discrete space-time transformations. However, only the action of the whole Lorentz group on them reveals their full symmetry structure. A good example that illustrates the covariance of Maxwell’s equations is provided by the electromagnetic fields of a point charge uniformly moving along a straight line.

Lorentz groupElectromagnetic fieldPhysicssymbols.namesakeMathematical optimizationClassical mechanicsSpacetimeMaxwell's equationssymbolsInhomogeneous electromagnetic wave equationMaxwell relationsLorentz forceAction (physics)
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On global solutions of the Maxwell-Dirac equations

1987

We prove, for the Maxwell-Dirac equations in 1+3 dimensions, that modified wave operators exist on a domain of small entire test functions of exponential type and that the Cauchy problem, inR+×R3, has a unique solution for each initial condition (att=0) which is in the image of the wave operator. The modification of the wave operator, which eliminates infrared divergences, is given by approximate solutions of the Hamilton-Jacobi equation, for a relativistic electron in an electromagnetic potential. The modified wave operator linearizes the Maxwell-Dirac equations to their linear part.

Momentum operatorElectromagnetic wave equationMathematical analysisStatistical and Nonlinear PhysicsInhomogeneous electromagnetic wave equationd'Alembert's formula35Q20Operator (computer programming)35L45Initial value problemD'Alembert operatorHyperbolic partial differential equation35P25Mathematical Physics81D25MathematicsCommunications in Mathematical Physics
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The time-harmonic Maxwell equations

1996

In this chapter we shall see that the solution of the time-harmonic Maxwell equations with real coefficients can be transformed to time independent partial differential equations with complex coefficients. Then we introduce a finite element approximation proposed in [Křižek, Neittaanmaki, 1989]. A similar technique is analyzed in [Křižek, Neittaanmaki, 1984b], [Monk, 1992a] (for fully time dependent problems see, e.g., [Monk 1992b,c]).

Physicssymbols.namesakeJefimenko's equationsClassical mechanicsTheoretical and experimental justification for the Schrödinger equationMaxwell's equationsMaxwell's equations in curved spacetimesymbolsInhomogeneous electromagnetic wave equationMatrix representation of Maxwell's equationsMaxwell relationsElectromagnetic tensor
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Maxwell’s Equations

2012

The empirical basis of electrodynamics is defined by Faraday’s law of induction, by Gauss’ law, by the law of Biot and Savart and by the Lorentz force and the principle of universal conservation of electric charge. These laws can be tested – confirmed or falsified – in realistic experiments. The integral form of the laws deals with physical objects that are one-dimensional, two-dimensional, or three-dimensional, that is to say, objects such as linear wires, conducting loops, spatial charge distributions, etc. Thus, the integral form depends, to some extent, on the concrete experimental set-up. To unravel the relationships between seemingly different phenomena, one must switch from the integ…

Physicssymbols.namesakeJefimenko's equationsClassical mechanicsTheoretical and experimental justification for the Schrödinger equationMaxwell's equationsMaxwell's equations in curved spacetimesymbolsMatrix representation of Maxwell's equationsInhomogeneous electromagnetic wave equationLorentz forceElectromagnetic tensor
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