Results 11 to 20 of about 5,337,814 (354)
Revisiting Schrödinger’s fourth-order, real-valued wave equation and the implication from the resulting energy levels [PDF]
Royal Society Open Science, 2023 In his seminal part IV, Annalen der Physik vol. 81, 1926 paper, Schrödinger has developed a clear understanding about the wave equation that produces the correct quadratic dispersion relation for matter-waves and he first presents a real-valued wave ...
Nicos Makris
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On the Fractional Wave Equation [PDF]
Mathematics, 2020 In this paper we study the time-fractional wave equation of order 1
Francesco Iafrate, Enzo Orsingher
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A hybrid explicit implicit staggered grid finite-difference scheme for the first-order acoustic wave equation modeling [PDF]
Scientific Reports, 2022 Implicit staggered-grid finite-difference (SGFD) methods are widely used for the first-order acoustic wave-equation modeling. The identical implicit SGFD operator is commonly used for all of the first-order spatial derivatives in the first-order acoustic
Wenquan Liang +3 more
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Relativistic wave equations [PDF]
Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1936 The classical relativistic connexion between the energy p t of a free article and its momentum p x , p y , p z , namely, p
P. A. M. Dirac
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Discovery of the exact 3D one-way wave equation [PDF]
Nature CommunicationsThe standard wave equation describing symmetrical wave propagation in all directions in three dimensions, was discovered by the French scientist d’Alembert, more than 250 years ago. In the 20th century it became important to search for ‘one-way’ versions
Kosmas L. Tsakmakidis +1 more
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On the biharmonic wave equation [PDF]
Pacific Journal of Mathematics, 1967 E. L. Roetman
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A generalised spheroidal wave equation
, 1928 1.1. The differential equation considered in this paper may be written in the form d / d ξ { (1-ξ²) d X/ d ξ } + { λ²ξ² - 2 p λξ - n 3²/1-ξ² + μ׳ } X = 0. (1) When p = 0 this equation becomes the equation giving the solution of ∇²X —λ²X = 0 in spheroidal
Alan Herries Wilson
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Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration
Fractal and Fractional, 2023 The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave
Sheikh Zain Majid +4 more
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Solving the frequency-domain acoustic VTI wave equation using physics-informed neural networks
Geophysical Journal International, 2021 Frequency-domain wavefield solutions corresponding to the anisotropic acoustic wave equation can be used to describe the anisotropic nature of the Earth. To solve a frequency-domain wave equation, we often need to invert the impedance matrix.
Chao Song, T. Alkhalifah, U. Waheed
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Spherical One-Way Wave Equation
Acoustics, 2021 The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it is necessary to achieve consistency between gradient, divergence and Laplace operators and to establish, beside the conventional radial Nabla operator ∂Φ/∂r ...
Oskar Bschorr, Hans-Joachim Raida
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