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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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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Exact solitary and periodic-wave solutions of the K(2,2) equation (defocusing branch) [PDF]
, 2010 An auxiliary elliptic equation method is presented for constructing exact solitary and periodic travelling-wave solutions of the K(2, 2) equation (defocusing branch). Some known results in the literature are recovered more efficiently, and some new exact
Cao, J. +4 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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Some periodic and solitary travelling-wave solutions of the short pulse equation [PDF]
, 2008 Exact periodic and solitary travelling-wave solutions of the short pulse equation are ...
Parkes, E.J.
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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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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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Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method [PDF]
, 2010 The homotopy analysis method is applied to the Degasperis-Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves.
Abbasbandy, S., Parkes, E.J.
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