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The American Mathematical Monthly, 1968
(1968). Separation of Variables. The American Mathematical Monthly: Vol. 75, No. 8, pp. 844-847.
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(1968). Separation of Variables. The American Mathematical Monthly: Vol. 75, No. 8, pp. 844-847.
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HUYGENS' PRINCIPLE AND SEPARATION OF VARIABLES
Reviews in Mathematical Physics, 2000We demonstrate a close relation between the algebraic structure of the (local) group of conformal transformations on a smooth Lorentzian manifold [Formula: see text] and the existence of nontrivial hierarchies of wave-type hyperbolic operators satisfying Huygens' principle on [Formula: see text].
Berest, Yuri, Winternitz, Pavel
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1999
In the previous chapter, some of the mathematical preliminaries were discussed. The principal physical equations which we will consider are those for heat flow, the wave equation and the potential equation of Laplace and are derived in the companion volume, Numerical methods for partial differential equations. These equations are very typical of second-
Gwynne A. Evans +2 more
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In the previous chapter, some of the mathematical preliminaries were discussed. The principal physical equations which we will consider are those for heat flow, the wave equation and the potential equation of Laplace and are derived in the companion volume, Numerical methods for partial differential equations. These equations are very typical of second-
Gwynne A. Evans +2 more
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2013
Three cardinal linear second-order partial differential equations have collectively driven the development of the entire subject. The first two we have already encountered: The wave equation describes vibrations and waves in continuous media, including sound waves, water waves, elastic waves, electromagnetic waves, and so on.
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Three cardinal linear second-order partial differential equations have collectively driven the development of the entire subject. The first two we have already encountered: The wave equation describes vibrations and waves in continuous media, including sound waves, water waves, elastic waves, electromagnetic waves, and so on.
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Separation of Variables in Electromagnetic Theory
Journal of Applied Physics, 1951Separability conditions are obtained for the partial differential equations of electromagnetic theory. Wave guide and antenna problems are expressed in terms of the vector Helmholtz equation, and solutions are indicated by use of the simple method of separation of variables without recourse to Green's functions.
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Separation of variables and Fourier series
1975In the applications which we will study in this chapter, we will be confronted with the following problem.
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Concerning Separation of Variables
Journal of the London Mathematical Society, 1967openaire +1 more source