wave equation
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1: 29.11 Lamé Wave Equation
2: 13.28 Physical Applications
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§13.28(i) Exact Solutions of the Wave Equation
►The reduced wave equation in paraboloidal coordinates, , , , can be solved via separation of variables , where …3: 10.73 Physical Applications
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►The Helmholtz equation, , follows from the wave equation
…This equation governs problems in acoustic and electromagnetic wave propagation.
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§10.73(ii) Spherical Bessel Functions
… ►In quantum mechanics the spherical Bessel functions arise in the solution of the Schrödinger wave equation for a particle in a central potential. …4: 30.10 Series and Integrals
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►Integrals and integral equations for are given in Arscott (1964b, §8.6), Erdélyi et al. (1955, §16.13), Flammer (1957, Chapter 5), and Meixner (1951).
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5: Bernard Deconinck
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►He has worked on integrable systems, algorithms for computations with Riemann surfaces, Bose-Einstein condensates, and methods to investigate the stability of solutions of nonlinear wave equations.
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6: 29.18 Mathematical Applications
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§29.18(i) Sphero-Conal Coordinates
►The wave equation … ►
29.18.7
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►The wave equation (29.18.1), when transformed to ellipsoidal
coordinates
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…where , , each satisfy the Lamé wave equation (29.11.1).
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7: Mark J. Ablowitz
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►Ablowitz is an applied mathematician who is interested in solutions of nonlinear wave equations.
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8: 30.14 Wave Equation in Oblate Spheroidal Coordinates
§30.14 Wave Equation in Oblate Spheroidal Coordinates
►§30.14(i) Oblate Spheroidal Coordinates
… ►The wave equation (30.13.7), transformed to oblate spheroidal coordinates , admits solutions of the form (30.13.8), where satisfies the differential equation … ►
30.14.9
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9: 28.33 Physical Applications
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►The wave equation
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28.33.1
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McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.