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The Leading Edge, 1987
The foundation of seismology is the theory of wave motion, a complicated concept that is still — after centuries of experiments and speculations by many of the very greatest scientists — an area of active research in many disciplines. Even simple forms of wave motion are difficult to describe verbally; but, ironically, the simplest type of wave is ...
Dean Clark, Enders A. Robinson
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The foundation of seismology is the theory of wave motion, a complicated concept that is still — after centuries of experiments and speculations by many of the very greatest scientists — an area of active research in many disciplines. Even simple forms of wave motion are difficult to describe verbally; but, ironically, the simplest type of wave is ...
Dean Clark, Enders A. Robinson
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The Laplace Equation and Wave Equation
1996In this chapter we introduce the central linear partial differential equations of the second order, the Laplace equation $$\Delta u = f$$ (0.1) and the wave equation $$\left (\frac{{\partial }^{2}} {\partial {t}^{2}} -\Delta\right )u = f.$$ (0.2) For flat Euclidean space \(\mathbb{R}^{n}\), the Laplace operator is defined by ...
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Study of the generalization of regularized long-wave equation
Nonlinear dynamics, 2022Yue Kai, Jialiang Ji, Zhixiang Yin
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The Massive Wave Equation in Asymptotically AdS Spacetimes
, 2012We consider the massive wave equation on asymptotically AdS spaces. We show that the timelike $${\fancyscript{F}}$$ behaves like a finite timelike boundary, on which one may impose the equivalent of Dirichlet, Neumann or Robin conditions for a range of ...
C. Warnick
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On Relativistic Wave Equations
Physical Review, 1947The problem of the relativistic invariance of a first-order wave equation with matrix coefficients ${\ensuremath{\beta}}_{k}$ is examined. It is found that it is intimately connected with the structure of the enveloping algebra of the $\ensuremath{\beta}$-matrices.
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On the geometry of the wave equation
Mathematical Proceedings of the Cambridge Philosophical Society, 1947An account is given of the transformation of coordinates and of absolute axial frames in Euclidean space and Galilean space-time. The connexion with Eddington's group of E-numbers is shown. The geometrical properties of Dirac's wave equation and of analogous equations in three dimensions are discussed in terms of absolute axial frames.
A. G. D. Watson, A. E. Ingham
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On equations for wave interactions [PDF]
Letters in Mathematical Physics, 1983 Starting with the representation of nonlinear evolution equations given by the author [cf. Problems on high energy physics and quantum field theory. I., Proc. Int. Semin., 5. All-Union Conf., Protvino (USSR), 93- 114 (1982)] four new nonlinear evolution equations arising usually in hydrodynamics and plasma physics are obtained.
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1971
(a) Let (a1) be an ordinary linear differential equation with constant coefficients.
Giovanni Prouse, Luigi Amerio
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(a) Let (a1) be an ordinary linear differential equation with constant coefficients.
Giovanni Prouse, Luigi Amerio
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1986
In this chapter we introduce the wave equation, formulate initial-boundary value problems, and prove uniqueness and existence via the spectral theorem. To get more information about the behaviour of the solutions, we have to study the spectrum of the underlying operators more carefully, which will be done in Chapter 4.
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In this chapter we introduce the wave equation, formulate initial-boundary value problems, and prove uniqueness and existence via the spectral theorem. To get more information about the behaviour of the solutions, we have to study the spectrum of the underlying operators more carefully, which will be done in Chapter 4.
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2020
In Chaps. 29 and 30, you have seen how Fourier and Laplace transforms help us solve Poisson’s equation and the diffusion equation. We turn our attention now to another very important equation of mathematical physics, the wave equation. As you might expect, this is a well-studied topic with a vast literature.
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In Chaps. 29 and 30, you have seen how Fourier and Laplace transforms help us solve Poisson’s equation and the diffusion equation. We turn our attention now to another very important equation of mathematical physics, the wave equation. As you might expect, this is a well-studied topic with a vast literature.
openaire +2 more sources