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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New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod
Results in Physics, 2018 This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs).
Aly R. Seadawy, Jalil Manafian
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Approximate Solutions of the Damped Wave Equation and Dissipative Wave Equation in Fractal Strings
Fractal and Fractional, 2019 In this paper, we apply the local fractional Laplace variational iteration method (LFLVIM) and the local fractional Laplace decomposition method (LFLDM) to obtain approximate solutions for solving the damped wave equation and dissipative wave equation ...
Dumitru Baleanu, Hassan Kamil Jassim
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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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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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A vector super Newell long-wave-short-wave equation and infinite conservation laws
Partial Differential Equations in Applied Mathematics, 2022 Based on the zero-curvature equation and Lenard recursion equations, we propose a vector super long-wave-short-wave hierarchy associated with an (n+2)×(n+2)matrix spectral problem.
Kedong Wang +3 more
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The Wave Equation with Energy Dependent Potential - the Linear Case [PDF]
مجلة جامعة النجاح للأبحاث العلوم الطبيعية, 2011 We summarize recent works devoted to energy dependent potentials. It concerns the class of potentials having a coupling constant depending linearly on the energy. Introduced in the Schrödinger equation, it produces non-linear effects.
Ronald Lombard
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The Q-Time Deformed Wave Equation
Journal of Mathematics, 2022 For q∈0,1, we introduce the q-time deformed wave equation; using the q-derivative, the solution of the q-time deformed wave equation is given. Also, we introduce the free-time wave equation which is a limit case q⟶0 of the q-time deformed wave equation.
Al-Nashri Al-Hossain Ahmad +1 more
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