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Relevant bibliographies by topics / Amplitude equation

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Academic literature on the topic 'Amplitude equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Amplitude equation"

1

Rauf, S., and J. A. Tataronis. "Resonant four-wave mixing of finite-amplitude Alfvén waves." Journal of Plasma Physics 55, no. 2 (1996): 173–80. http://dx.doi.org/10.1017/s0022377800018766.

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Using the derivative nonlinear SchrÖdinger equation, resonant four-wave mixing of finite-amplitude Alfvén waves is explored in this paper. The evolution equations governing the amplitudes of the interacting waves and the conservation relations ale derived from the basic equation. These evolution equations are used to study parametric amplification and oscillation of two small-amplitude Alfvén waves due to two large-amplitude pump (Alfvén) waves. It is also shown that three pump waves can mix together to generate a low-frequency Alfven wave in a dissipative plasma.

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Zhang, Yu, Guanquan Zhang, and Norman Bleistein. "Theory of true-amplitude one-way wave equations and true-amplitude common-shot migration." GEOPHYSICS 70, no. 4 (2005): E1—E10. http://dx.doi.org/10.1190/1.1988182.

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One-way wave operators are powerful tools for forward modeling and migration. Here, we describe a recently developed true-amplitude implementation of modified one-way operators and present some numerical examples. By “true-amplitude” one-way forward modeling we mean that the solutions are dynamically correct as well as kinematically correct. That is, ray theory applied to these equations yields the upward- and downward-traveling eikonal equations of the full wave equation, and the amplitude satisfies the transport equation of the full wave equation. The solutions of these equations are used in

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Vivas, Flor A., and Reynam C. Pestana. "True-amplitude one-way wave equation migration in the mixed domain." GEOPHYSICS 75, no. 5 (2010): S199—S209. http://dx.doi.org/10.1190/1.3478574.

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One-way wave equation migration is a powerful imaging tool for locating accurately reflectors in complex geologic structures; however, the classical formulation of one-way wave equations does not provide accurate amplitudes for the reflectors. When dynamic information is required after migration, such as studies for amplitude variation with angle or when the correct amplitudes of the reflectors in the zero-offset images are needed, some modifications to the one-way wave equations are required. The new equations, which are called “true-amplitude one-way wave equations,” provide amplitudes that

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Feng, Zongcai, and Gerard Schuster. "True-amplitude linearized waveform inversion with the quasi-elastic wave equation." GEOPHYSICS 84, no. 6 (2019): R827—R844. http://dx.doi.org/10.1190/geo2019-0116.1.

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We present a quasi-elastic wave equation as a function of the pressure variable, which can accurately model PP reflections with elastic amplitude variation with offset effects under the first-order Born approximation. The kinematic part of the quasi-elastic wave equation accurately models the propagation of P waves, whereas the virtual-source part, which models the amplitudes of reflections, is a function of the perturbations of density and Lamé parameters [Formula: see text] and [Formula: see text]. The quasi-elastic wave equation generates a scattering radiation pattern that is exactly the s

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Kovachev, Lubomir M. "Optical vortices in dispersive nonlinear Kerr-type media." International Journal of Mathematics and Mathematical Sciences 2004, no. 18 (2004): 949–67. http://dx.doi.org/10.1155/s0161171204301018.

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The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. Critical values of parameters to observe different linear and nonlinear effects are determined. The obtained amplitude equations are a vector version of3D+1nonlinear Schrödinger equation (VNSE) describing the evolution of slowly varying ampl

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MOSLEM, W. M. "Propagation of ion acoustic waves in a warm multicomponent plasma with an electron beam." Journal of Plasma Physics 61, no. 2 (1999): 177–89. http://dx.doi.org/10.1017/s0022377898007429.

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The nonlinear wave structures of small-amplitude ion acoustic waves in a warm plasma with adiabatic negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures) in the vicinity of the critical negative-ion density are investigated using reductive perturbation method. The basic set of equations is reduced to an evolution equation that includes quadratic and cubic nonlinearities. The effective potential of this equation agrees exactly, for small wave amplitudes, with the Sagdeev potential obtained from the original fluid equations using a pseud

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Hutahaean, Syawaluddin. "Wavelength and Wave Period Relationship with Wave Amplitude: A Velocity Potential Formulation." International Journal of Advanced Engineering Research and Science 9, no. 8 (2022): 387–93. http://dx.doi.org/10.22161/ijaers.98.44.

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In this study, the equation that expresses the explicit relationship between the wave number and wave amplitude, as well as wave period and wave amplitude are established. The wave number and the wave period are calculated solely using the input wave amplitude. The equation is formulated with the velocity potential of the solution to Laplace’s equation to the hydrodynamic conservation equations, such as the momentum equilibrium equation, Euler Equation for conservation of momentum, and by working on the kinematic bottom and free surface boundary condition.In this study, the equation that expre

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Meis, Constantin, and Pierre Richard Dahoo. "Vector potential quantization and the photon intrinsic electromagnetic properties: Towards nondestructive photon detection." International Journal of Quantum Information 15, no. 08 (2017): 1740003. http://dx.doi.org/10.1142/s0219749917400032.

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We employ here the enhancement of the vector potential amplitude quantization at a single photon state. The analysis of the general solution of the vector potential, obtained by resolving Maxwell’s equations, implies that the amplitude is proportional to the angular frequency. The photon vector potential function αkλ(r,t) can be written in the plane wave representation satisfying the classical wave propagation equation, Schrödinger’s equation for the energy with the relativistic massless field Hamiltonian and a linear time-dependent equation for the vector potential amplitude operator. Thus, t

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Angus, D. A. "True amplitude corrections for a narrow-angle one-way elastic wave equation." GEOPHYSICS 72, no. 2 (2007): T19—T26. http://dx.doi.org/10.1190/1.2430694.

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Wavefield extrapolators using one-way wave equations are computationally efficient methods for accurate traveltime modeling in laterally heterogeneous media, and have been used extensively in many seismic forward modeling and migration problems. However, most leading-order, one-way wave equations do not simulate waveform amplitudes accurately and this is primarily because energy flux is not accounted for correctly. I review the derivation of a leading-order, narrow-angle, one-way elastic wave equation for 3D media. I derive correction terms that enable energy-flux normalization and introduce a

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Zhang, Yu, Guanquan Zhang, and Norman Bleistein. "True amplitude wave equation migration arising from true amplitude one-way wave equations." Inverse Problems 19, no. 5 (2003): 1113–38. http://dx.doi.org/10.1088/0266-5611/19/5/307.

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Dissertations / Theses on the topic "Amplitude equation"

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Klepel, Konrad Verfasser], and Dirk [Akademischer Betreuer] [Blömker. "Amplitude equations for the generalised Swift-Hohenberg equation with noise / Konrad Klepel. Betreuer: Dirk Blömker." Augsburg : Universität Augsburg, 2015. http://d-nb.info/107770562X/34.

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Harris, Derek. "A study of a nonlinear amplitude equation modelling spherical couette flow." Thesis, University of Exeter, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367377.

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Punekar, Jyothika Narasimha. "Numerical simulation of nonlinear random noise." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243151.

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Blockley, Edward William. "Nonlinear solutions of the amplitude equations governing fluid flow in rotating spherical geometries." Thesis, University of Exeter, 2008. http://hdl.handle.net/10036/41950.

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We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes the form of roughly square axisymmetric Taylor vortices which arise in the vicinity of the equator and are modulated on a latitudinal length scale large compared to the gap width but small compared to the shell radii. At the heart of the difficulties faced is the presence of phase mixing in the system, characterised by a non-zero frequency gradient at the equator and the tend

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Petrovic, Milena. "Effects of the Object’s Mass and Distance on the Location of Preferred Critical Boundary, Discomfort, and Muscle Activation during a Seated Reaching Task." Miami University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=miami1343567265.

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Belayouni, Nidhal. "Nouveaux algorithmes efficaces de modélisation 2D et 3D : Temps des premières arrivées, angles à la source et amplitudes." Phd thesis, Ecole Nationale Supérieure des Mines de Paris, 2013. http://pastel.archives-ouvertes.fr/pastel-00871200.

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Les temps de trajet, amplitudes et angles à la source des ondes sismiques sont utilisés dans de nombreuses applications telles que la migration, la tomographie, l'estimation de la sensibilité de détection et la localisation des microséismes. Dans le contexte de la microsismicité, il est nécessaire de calculer en quasi temps réel ces attributs avec précision. Nous avons développé ici un ensemble d'algorithmes rapides et précis en 3D pour des modèles à fort contraste de vitesse.Nous présentons une nouvelle méthode pour calculer les temps de trajet, les amplitudes et les angles à la source des on

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Belayouni, Nidhal. "Nouveaux algorithmes efficaces de modélisation 2D et 3D : Temps des premières arrivées, angles à la source et amplitudes." Electronic Thesis or Diss., Paris, ENMP, 2013. http://www.theses.fr/2013ENMP0012.

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Les temps de trajet, amplitudes et angles à la source des ondes sismiques sont utilisés dans de nombreuses applications telles que la migration, la tomographie, l'estimation de la sensibilité de détection et la localisation des microséismes. Dans le contexte de la microsismicité, il est nécessaire de calculer en quasi temps réel ces attributs avec précision. Nous avons développé ici un ensemble d'algorithmes rapides et précis en 3D pour des modèles à fort contraste de vitesse.Nous présentons une nouvelle méthode pour calculer les temps de trajet, les amplitudes et les angles à la source des on

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Tanré, Etienne. "Étude probabiliste des équations de SmoluchowskiSchéma d'Euler pour des fonctionnellesAmplitude du mouvement brownien avec dérive." Nancy 1, 2001. http://www.theses.fr/2001NAN10178.

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Cette thèse est composée de trois parties indépendantes. La première partie est une étude probabiliste des équations de coagulation de Smoluchowski. Une représentation des solutions est établie grâce à des processus de branchement de type Galton-Watson. On montre par ailleurs une correspondance entre les noyaux additif et multiplicatif. Le comportement asymptotique des solutions après renormalisation est également étudié. Enfin, on construit un processus, solution d'une E. D. S. Non-linéaire gouvernée par un processus de Poisson, dont les marginales temporelles sont solutions des équations de

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Sunny, Danish Ali [Verfasser], and Guido [Akademischer Betreuer] Schneider. "Failure of amplitude equations / Danish Ali Sunny ; Betreuer: Guido Schneider." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2016. http://d-nb.info/1124465987/34.

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NINET, ALAIN. "Amplitude de diffusion pour les equations de l'elasticite et de maxwell." Reims, 1998. http://www.theses.fr/1998REIMS019.

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Cette these est constituee de deux parties. Dans la premiere, on etudie l'amplitude de diffusion pour le systeme de l'elasticite et celui de maxwell avec une perturbation compacte. Nous verrons egalement certaines techniques communes a ces deux systemes : un principe d'absorption limite et des projecteurs semi-classiques pour des systemes, et l'etude d'un produit scalaire faisant intervenir une resolvante limite et des fonctions lagrangiennes. Dans la seconde partie, on definit une notion d'ensemble de frequence associe a une suite de representations d'un groupe de lie compact en utilisant des

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Books on the topic "Amplitude equation"

1

Amplitude Equations for Stochastic Partial Differential Equations. World Scientific Publishing Co Pte Ltd, 2007.

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2

Steane, Andrew M. Relativity Made Relatively Easy Volume 2. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895646.001.0001.

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This is a textbook on general relativity and cosmology for a physics undergraduate or an entry-level graduate course. General relativity is the main subject; cosmology is also discussed in considerable detail (enough for a complete introductory course). Part 1 introduces concepts and deals with weak-field applications such as gravitation around ordinary stars, gravimagnetic effects and low-amplitude gravitational waves. The theory is derived in detail and the physical meaning explained. Sources, energy and detection of gravitational radiation are discussed. Part 2 develops the mathematics of d

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Horing, Norman J. Morgenstern. Retarded Green’s Functions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0005.

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Chapter 5 introduces single-particle retarded Green’s functions, which provide the probability amplitude that a particle created at (x, t) is later annihilated at (x′,t′). Partial Green’s functions, which represent the time development of one (or a few) state(s) that may be understood as localized but are in interaction with a continuum of states, are discussed and applied to chemisorption. Introductions are also made to the Dyson integral equation, T-matrix and the Dirac delta-function potential, with the latter applied to random impurity scattering. The retarded Green’s function in the prese

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Mann, Peter. Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0019.

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This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and dis

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Amplitude Equations for Stochastic Partial Differential Equations. Interdisciplinary Mathematical Sciences, Volume 3. World Scientific Publishing Co Pte Ltd, 2007.

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Amplitude Equations for Stochastic Partial Differential Equations (Interdisciplinary Mathematical Sciences) (Interdisciplinary Mathematical Sciences). World Scientific Publishing Company, 2007.

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7

El Karoui, Noureddine. Algebraic geometry and matrix models. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.29.

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This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first desc

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8

Nonlinear interaction of detuned instability waves in boundary-layer transition: Amplitude equations. National Aeronautics and Space Administration, Lewis Research Center, 1998.

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9

Phase characteristics and time responses of unknown linear systems determined from measured CW amplitude data. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1991.

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10

T. Wave Phenomena. Courier Dover Publications, 2014.

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Book chapters on the topic "Amplitude equation"

1

Elmer, F. J., and T. Christen. "The Nonlocal Amplitude Equation." In Partially Intergrable Evolution Equations in Physics. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0591-7_26.

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Norris, Andrew N. "Finite-Amplitude Waves in Solids." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_9.

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AbstractThe theoretical foundation for weakly nonlinear elastic waves in isotropic solids is developed. Lagrangian coordinates are used to obtain the equation of motion in terms of the Piola-Kirchhoff stress tensor, which is a function of the strain energy density. Notations employed for elastic constants in different expansions of the strain energy density are related to those introduced by Landau and Lifshitz. Use of the acoustoelastic effect to determine the third-order elastic constants is described. Solutions are presented for second-harmonic generation in a longitudinal plane wave. Final

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Gurbatov, Sergey N., and Oleg V. Rudenko. "Statistical Phenomena." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_13.

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AbstractStatistical analysis is applied to phenomena associated with propagation of random nonlinear acoustic waveforms in homogeneous media. Following presentation of the nonlinear evolution equation and relevant statistical functions, basic phenomena in nonlinear noise fields are described for an initially quasi-harmonic signal with random amplitude and phase modulation. An expression is presented for the intensity of the harmonics generated by a source radiating narrowband noise. Examples are provided illustrating the widening of the frequency spectrum associated with propagation of broadba

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Misbah, Chaouqi. "Universal Amplitude Equation in the Neighborhood of a Hopf Bifurcation." In Complex Dynamics and Morphogenesis. Springer Netherlands, 2016. http://dx.doi.org/10.1007/978-94-024-1020-4_6.

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Pandey, Neeraj, M. P. Singh, Amitava Ghsoh, and Kedar Khare. "Amplitude Object Reconstruction at Multiple Planes Using Transport of Intensity Equation." In Springer Proceedings in Physics. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9259-1_147.

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Blackstock, David T., Mark F. Hamilton, and Allan D. Pierce. "Progressive Waves in Lossless and Lossy Fluids." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_4.

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AbstractThis chapter analyzes nonlinear progressive waves, and primarily plane waves. Following presentation of exact implicit solutions for ideal fluids, approximate explicit solutions are obtained for harmonic generation in lossless and lossy fluids. The Rankine-Hugoniot relations are derived for shocks of arbitrary strength, followed by their quadratic approximation for weak shocks. The history and solutions of the Burgers equation are presented, including the rise time and thickness of weak shocks. Progressive plane-wave solutions based on weak-shock theory are transformed to describe cyli

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Hamilton, Mark F. "Sound Beams." In Nonlinear Acoustics. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-58963-8_8.

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AbstractDiffraction in sound beams is analyzed using the KZK nonlinear parabolic wave equation. General integral solutions are presented for generation of the second harmonic, sum, and difference frequencies in weakly nonlinear axisymmetric sound beams. Analytical solutions are obtained for sources with Gaussian amplitude distributions, both unfocused and focused. Asymptotic solutions are presented for far-field radiation from circular pistons, and the appearance of additional sidelobes is explained. Solutions for difference-frequency radiation in the far field of a parametric array, and the a

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Chadan, K., P. C. Sabatier, and R. G. Newton. "Potentials from the Scattering Amplitude at Fixed Energy: General Equation and Mathematical Tools." In Inverse Problems in Quantum Scattering Theory. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-83317-5_11.

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Newton, P. K., and R. M. Axel. "Amplitude Equation Models for the Interaction of Shocks with Nonlinear Dispersive Wave Envelopes." In Selected Topics in Nonlinear Wave Mechanics. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0095-6_2.

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Soumekh, Mehrdad. "Phase Reconstruction from Amplitude Based on the Rytov Transformation of the Wave Equation." In Acoustical Imaging. Springer US, 1989. http://dx.doi.org/10.1007/978-1-4613-0791-4_33.

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Conference papers on the topic "Amplitude equation"

1

Joncour, F., J. Svay-Lucas, G. Lumbare, and B. Duquet. "True Amplitude Wave Equation Migration." In 67th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2005. http://dx.doi.org/10.3997/2214-4609-pdb.1.f046.

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Kiyashchenko, D., R. E. Plessix, B. Kashtan, and V. Troyan. "Improved Amplitude Multi-One-Way Wave-Equation Migration." In 67th EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2005. http://dx.doi.org/10.3997/2214-4609-pdb.1.f047.

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Pu, Yu, Gang Liu, Diancheng Wang, Hui Huang, and Ping Wang. "Wave-equation traveltime and amplitude for Kirchhoff migration." In First International Meeting for Applied Geoscience & Energy. Society of Exploration Geophysicists, 2021. http://dx.doi.org/10.1190/segam2021-3583642.1.

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Dakova, A., D. Dakova, and L. Kovachev. "Comparison of soliton solutions of the nonlinear Schrödinger equation and the nonlinear amplitude equation." In Eighteenth International School on Quantum Electronics: Laser Physics and Applications, edited by Tanja Dreischuh, Sanka Gateva, and Alexandros Serafetinides. SPIE, 2015. http://dx.doi.org/10.1117/12.2177906.

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Sava, Paul, Biondo Biondi, and Sergey Fomel. "Amplitude‐preserved common image gathers by wave‐equation migration." In SEG Technical Program Expanded Abstracts 2001. Society of Exploration Geophysicists, 2001. http://dx.doi.org/10.1190/1.1816598.

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Angus, Doug. "Amplitude corrections for a narrow‐angle elastic wave equation." In SEG Technical Program Expanded Abstracts 2006. Society of Exploration Geophysicists, 2006. http://dx.doi.org/10.1190/1.2372481.

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Vivas, Flor A., and Reynam C. Pestana. "True-amplitude one-way wave equation migration in heterogenoues media." In 10th International Congress of the Brazilian Geophysical Society & EXPOGEF 2007, Rio de Janeiro, Brazil, 19-23 November 2007. Society of Exploration Geophysicists and Brazilian Geophysical Society, 2007. http://dx.doi.org/10.1190/sbgf2007-327.

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Amazonas, D., R. Aleixo, J. Schleicher, J. Costa, A. Novais, and G. Melo. "Including lateral velocity variations into true-amplitude wave-equation migration." In 11th International Congress of the Brazilian Geophysical Society & EXPOGEF 2009, Salvador, Bahia, Brazil, 24-28 August 2009. Society of Exploration Geophysicists and Brazilian Geophysical Society, 2009. http://dx.doi.org/10.1190/sbgf2009-315.

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Feng, Zongcai, and Gerard Schuster. "True-amplitude waveform inversion with the quasi-elastic wave equation." In SEG Technical Program Expanded Abstracts 2019. Society of Exploration Geophysicists, 2019. http://dx.doi.org/10.1190/segam2019-3214072.1.

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Jin, Hu, and John Etgen. "Evaluating Kirchhoff migration using wave-equation generated maximum amplitude traveltimes." In SEG Technical Program Expanded Abstracts 2020. Society of Exploration Geophysicists, 2020. http://dx.doi.org/10.1190/segam2020-3425618.1.

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Reports on the topic "Amplitude equation"

1

Tzenov, S. I. Formation of patterns in intense hadron beams. The amplitude equation approach. Office of Scientific and Technical Information (OSTI), 2000. http://dx.doi.org/10.2172/753290.

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Lindesay, James V. Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations. Office of Scientific and Technical Information (OSTI), 2002. http://dx.doi.org/10.2172/799023.

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