Relevant bibliographies by topics / Inverse Scattering Transform

Academic literature on the topic 'Inverse Scattering Transform'

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Published: 4 June 2021
Last updated: 24 January 2023

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Journal articles on the topic "Inverse Scattering Transform"

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Steudel, H., and D. J. Kaup. "Inverse scattering transform on a finite interval." Journal of Physics A: Mathematical and General 32, no. 34 (August 13, 1999): 6219–31. http://dx.doi.org/10.1088/0305-4470/32/34/308.

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Vekslerchik, V. E. "Inverse scattering transform for the nonlinear -model." Inverse Problems 12, no. 4 (August 1, 1996): 517–34. http://dx.doi.org/10.1088/0266-5611/12/4/012.

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Desbruslais, Stephen. "Inverse Scattering Transform for Soliton Transmission Analysis." Optical Fiber Technology 2, no. 4 (October 1996): 319–42. http://dx.doi.org/10.1006/ofte.1996.0037.

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Teschl, Gerald. "Inverse Scattering Transform for the Toda Hierarchy." Mathematische Nachrichten 202, no. 1 (1999): 163–71. http://dx.doi.org/10.1002/mana.19992020113.

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Fokas, A. S. "Inverse scattering transform, inverse data and nonlinear evolution equations in multidimensions." Physica D: Nonlinear Phenomena 28, no. 1-2 (September 1987): 223. http://dx.doi.org/10.1016/0167-2789(87)90145-x.

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Cable, J. R., and A. C. Albrecht. "A direct inverse transform for resonance Raman scattering." Journal of Chemical Physics 84, no. 9 (May 1986): 4745–54. http://dx.doi.org/10.1063/1.449958.

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Turitsyna, Elena G., and Sergei K. Turitsyn. "Digital signal processing based on inverse scattering transform." Optics Letters 38, no. 20 (October 11, 2013): 4186. http://dx.doi.org/10.1364/ol.38.004186.

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Constantin, Adrian, Rossen I. Ivanov, and Jonatan Lenells. "Inverse scattering transform for the Degasperis–Procesi equation." Nonlinearity 23, no. 10 (August 20, 2010): 2559–75. http://dx.doi.org/10.1088/0951-7715/23/10/012.

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Constantin, Adrian, Vladimir S. Gerdjikov, and Rossen I. Ivanov. "Inverse scattering transform for the Camassa–Holm equation." Inverse Problems 22, no. 6 (October 20, 2006): 2197–207. http://dx.doi.org/10.1088/0266-5611/22/6/017.

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Villarroel, J. "Yang-Mills equations and the inverse scattering transform." Journal of Physics A: Mathematical and General 24, no. 15 (August 7, 1991): 3587–92. http://dx.doi.org/10.1088/0305-4470/24/15/025.

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Dissertations / Theses on the topic "Inverse Scattering Transform"

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Kusiak, Steven J. "The scattering support and the inverse scattering problem at fixed frequency /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/6779.

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歐陽天祥 and Yeung Tin-cheung Au. "An investigation of the inverse scattering method under certain nonvanishing conditions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1987. http://hub.hku.hk/bib/B31231056.

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Au, Yeung Tin-cheung. "An investigation of the inverse scattering method under certain nonvanishing conditions /." [Hong Kong : University of Hong Kong], 1987. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12358514.

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Xiao, Jingni. "Theoretical advances on scattering theory, fractional operators and their inverse problems." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/513.

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Inverse problems arise in numerous fields of science and engineering where one tries to find out the desired information of an unknown object or the cause of an observed effect. They are of fundamental importance in many areas including radar and sonar applications, nondestructive testing, image processing, medical imaging, remote sensing, geophysics and astronomy among others. This study is concerned with three issues in scattering theory, fractional operators, as well as some of their inverse problems. The first topic is scattering problems for electromagnetic waves governed by Maxwell equations. It will be proved in the current study that an inhomogeneous EM medium with a corner on its support always scatters by assuming certain regularity and admissible conditions. This result implies that one cannot achieve invisibility for such materials. In order to verify the result, an integral of solutions to certain interior transmission problem is to be analyzed, and complex geometry optics solutions to corresponding Maxwell equations with higher order estimate for the residual will be constructed. The second problem involves the linearized elastic or seismic wave scattering described by the Lamei system. We will consider the elastic or seismic body wave which is composed of two different type of sub-waves, that is, the compressional or primary (P-) and the shear or secondary (S-) waves. We shall prove that the P- and the S-components of the total wave can be completely decoupled under certain geometric and boundary conditions. This is a surprising finding since it is known that the P- and the S-components of the elastic or seismic body wave are coupled in general. Results for decoupling around local boundary pieces, for boundary value problems, and for scattering problems are to be established. This decoupling property will be further applied to derive uniqueness and stability for the associated inverse problem of identifying polyhedral elastic obstacles by an optimal number of scattering measurements. Lastly, we consider a type of fractional (and nonlocal) elliptic operators and the associated Calderoin problem. The well-posedness for a kind of forward problems concerning the fractional operator will be established. As a consequence, the corresponding Dirichlet to Neumann map with certain mapping property is to be defined. As for the inverse problem, it will be shown that a potential can be uniquely identified by local Cauchy data of the associated nonlocal operator, in dimensions larger than or equal to two.
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Waldspurger, Irène. "Wavelet transform modulus : phase retrieval and scattering." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0036/document.

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Les tâches qui consistent à comprendre automatiquement le contenu d’un signal naturel, comme une image ou un son, sont en général difficiles. En effet, dans leur représentation naïve, les signaux sont des objets compliqués, appartenant à des espaces de grande dimension. Représentés différemment, ils peuvent en revanche être plus faciles à interpréter. Cette thèse s’intéresse à une représentation fréquemment utilisée dans ce genre de situations, notamment pour analyser des signaux audio : le module de la transformée en ondelettes. Pour mieux comprendre son comportement, nous considérons, d’un point de vue théorique et algorithmique, le problème inverse correspondant : la reconstruction d’un signal à partir du module de sa transformée en ondelettes. Ce problème appartient à une classe plus générale de problèmes inverses : les problèmes de reconstruction de phase. Dans un premier chapitre, nous décrivons un nouvel algorithme, PhaseCut, qui résout numériquement un problème de reconstruction de phase générique. Comme l’algorithme similaire PhaseLift, PhaseCut utilise une relaxation convexe, qui se trouve en l’occurence être de la même forme que les relaxations du problème abondamment étudié MaxCut. Nous comparons les performances de PhaseCut et PhaseLift, en termes de précision et de rapidité. Dans les deux chapitres suivants, nous étudions le cas particulier de la reconstruction de phase pour la transformée en ondelettes. Nous montrons que toute fonction sans fréquence négative est uniquement déterminée (à une phase globale près) par le module de sa transformée en ondelettes, mais que la reconstruction à partir du module n’est pas stable au bruit, pour une définition forte de la stabilité. On démontre en revanche une propriété de stabilité locale. Nous présentons également un nouvel algorithme de reconstruction de phase, non-convexe, qui est spécifique à la transformée en ondelettes, et étudions numériquement ses performances. Enfin, dans les deux derniers chapitres, nous étudions une représentation plus sophistiquée, construite à partir du module de transformée en ondelettes : la transformée de scattering. Notre but est de comprendre quelles propriétés d’un signal sont caractérisées par sa transformée de scattering. On commence par démontrer un théorème majorant l’énergie des coefficients de scattering d’un signal, à un ordre donné, en fonction de l’énergie du signal initial, convolé par un filtre passe-haut qui dépend de l’ordre. On étudie ensuite une généralisation de la transformée de scattering, qui s’applique à des processus stationnaires. On montre qu’en dimension finie, cette transformée généralisée préserve la norme. En dimension un, on montre également que les coefficients de scattering généralisés d’un processus caractérisent la queue de distribution du processus
Automatically understanding the content of a natural signal, like a sound or an image, is in general a difficult task. In their naive representation, signals are indeed complicated objects, belonging to high-dimensional spaces. With a different representation, they can however be easier to interpret. This thesis considers a representation commonly used in these cases, in particular for theanalysis of audio signals: the modulus of the wavelet transform. To better understand the behaviour of this operator, we study, from a theoretical as well as algorithmic point of view, the corresponding inverse problem: the reconstruction of a signal from the modulus of its wavelet transform. This problem belongs to a wider class of inverse problems: phase retrieval problems. In a first chapter, we describe a new algorithm, PhaseCut, which numerically solves a generic phase retrieval problem. Like the similar algorithm PhaseLift, PhaseCut relies on a convex relaxation of the phase retrieval problem, which happens to be of the same form as relaxations of the widely studied problem MaxCut. We compare the performances of PhaseCut and PhaseLift, in terms of precision and complexity. In the next two chapters, we study the specific case of phase retrieval for the wavelet transform. We show that any function with no negative frequencies is uniquely determined (up to a global phase) by the modulus of its wavelet transform, but that the reconstruction from the modulus is not stable to noise, for a strong notion of stability. However, we prove a local stability property. We also present a new non-convex phase retrieval algorithm, which is specific to the case of the wavelet transform, and we numerically study its performances. Finally, in the last two chapters, we study a more sophisticated representation, built from the modulus of the wavelet transform: the scattering transform. Our goal is to understand which properties of a signal are characterized by its scattering transform. We first prove that the energy of scattering coefficients of a signal, at a given order, is upper bounded by the energy of the signal itself, convolved with a high-pass filter that depends on the order. We then study a generalization of the scattering transform, for stationary processes. We show that, in finite dimension, this generalized transform preserves the norm. In dimension one, we also show that the generalized scattering coefficients of a process characterize the tail of its distribution
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Scoufis, George. "An Application of the Inverse Scattering Transform to some Nonlinear Singular Integro-Differential Equations." University of Sydney, Mathematics and Statistics, 1999. http://hdl.handle.net/2123/412.

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ABSTRACT The quest to model wave propagation in various physical systems has produced a large set of diverse nonlinear equations. Nonlinear singular integro-differential equations rank amongst the intricate nonlinear wave equations available to study the classical problem of wave propagation in physical systems. Integro-differential equations are characterized by the simultaneous presence of integration and differentiation in a single equation. Substantial interest exists in nonlinear wave equations that are amenable to the Inverse Scattering Transform (IST). The IST is an adroit mathematical technique that delivers analytical solutions of a certain type of nonlinear equation: soliton equation. Initial value problems of numerous physically significant nonlinear equations have now been solved through elegant and novel implementations of the IST. The prototype nonlinear singular integro-differential equation receptive to the IST is the Intermediate Long Wave (ILW) equation, which models one-dimensional weakly nonlinear internal wave propagation in a density stratified fluid of finite total depth. In the deep water limit the ILW equation bifurcates into a physically significant nonlinear singular integro-differential equation known as the 'Benjamin-Ono' (BO) equation; the shallow water limit of the ILW equation is the famous Korteweg-de Vries (KdV) equation. Both the KdV and BO equations have been solved by dissimilar implementations of the IST. The Modified Korteweg-de Vries (MKdV) equation is a nonlinear partial differential equation, which was significant in the historical development of the IST. Solutions of the MKdV equation are mapped by an explicit nonlinear transformation known as the 'Miura transformation' into solutions of the KdV equation. Historically, the Miura transformation manifested the intimate connection between solutions of the KdV equation and the inverse problem for the one-dimensional time independent Schroedinger equation. In light of the MKdV equation's significance, it is natural to seek 'modified' versions of the ILW and BO equations. Solutions of each modified nonlinear singular integro-differential equation should be mapped by an analogue of the original Miura transformation into solutions of the 'unmodified' equation. In parallel with the limiting cases of the ILW equation, the modified version of the ILW equation should reduce to the MKdV equation in the shallow water limit and to the modified version of the BO equation in the deep water limit. The Modified Intermediate Long Wave (MILW) and Modified Benjamin-Ono (MBO) equations are the two nonlinear singular integro-differential equations that display all the required attributes. Several researchers have shown that the MILW and MBO equations exhibit the signature characteristic of soliton equations. Despite the significance of the MILW and MBO equations to soliton theory, and the possible physical applications of the MILW and MBO equations, the initial value problems for these equations have not been solved. In this thesis we use the IST to solve the initial value problems for the MILW and MBO equations on the real-line. The only restrictions that we place on the initial values for the MILW and MBO equations are that they be real-valued, sufficiently smooth and decay to zero as the absolute value of the spatial variable approaches large values.
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Scoufis, George. "An application of the inverse scattering transform to some nonlnear singular integro-differential equations." Connect to full text, 1999. http://hdl.handle.net/2123/412.

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Thesis (Ph. D.)--University of Sydney, 1999.
Title from title screen (viewed Apr. 21, 2008). Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliography. Also available in print form.
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Renger, Walter. "Limits of soliton solutions /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9823316.

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Rigaud, Gaël. "Study of generalized Radon transforms and applications in Compton scattering tomography." Phd thesis, Université de Cergy Pontoise, 2013. http://tel.archives-ouvertes.fr/tel-00945739.

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Since the advent of the first ionizing radiation imaging devices initiated by Godfrey Newbold Hounsfield and Allan MacLeod Cormack, Nobel Prizes in 1979, the requirement for new non-invasive imaging techniques has grown. These techniques rely upon the properties of penetration in the matter of X and gamma radiation for detecting a hidden structure without destroying the illuminated environment. They are used in many fields ranging from medical imaging to non-destructive testing through. However, the techniques used so far suffer severe degradation in the quality of measurement and reconstructed images. Usually approximated by a noise, these degradations require to be compensated or corrected by collimating devices and often expensive filtering. These degradation is mainly due to scattering phenomena which may constitute up to 80% of the emitted radiation in biological tissue. In the 80's a new concept has emerged to circumvent this difficulty : the Compton scattering tomography (CST).This new approach proposes to measure the scattered radiation considering energy ranges ( 140-511 keV) where the Compton effect is the phenomenon of leading broadcast. The use of such imaging devices requires a deep understanding of the interactions between radiation and matter to propose a modeling, consistent with the measured data, which is essential to image reconstruction. In conventional imaging systems (which measure the primary radiation) the Radon transformdefined on the straight lines emerged as the natural modeling. But in Compton scattering tomography, the measured information is related to the scattering energy and thus the scattering angle. Thus the circular geometry induced by scattering phenomenon makes the classical Radon transform inadequate.In this context, it becomes necessary to provide such Radon transforms on broader geometric manifolds.The study of the Radon transform on new manifolds of curves becomes necessary to provide theoretical needs for new imaging techniques. Cormack, himself, was the first to extend the properties of the conventional Radon transform of a family of curves of the plane. Thereafter several studies have been done in order to study the Radon transform defined on different varieties of circles, spheres, broken lines ... . In 1994 S.J. Norton proposed the first modality in Compton scattering tomography modeled by a Radon transform on circular arcs, the CART1 here. In 2010, Nguyen and Truong established the inversion formula of a Radon transform on circular arcs, CART2, to model the image formation in a new modality in Compton scattering tomography. The geometry involved in the integration support of new modalities in Compton scattering tomography lead them to demonstrate the invertibility of the Radon transform defined on a family of Cormack-type curves, called C_alpha. They illustrated the inversion procedure in the case of a new transform, the CART3, modeling a new modeling of Compton scattering tomography. Based on the work of Cormack and Truong and Nguyen, we propose to establish several properties of the Radon transform on the family C_alpha especially on C1. We have thus demonstrated two inversion formulae that reconstruct the original image via its circular harmonic decomposition and itscorresponding transform. These formulae are similar to those established by Truong and Nguyen. We finally established the well-known filtered back projection and singular value decomposition in the case alpha = 1. All results established in this study provide practical problems of image reconstruction associated with these new transforms. In particular we were able to establish new inversion methods for transforms CART1,2,3 as well as numerical approaches necessary for the implementation of these transforms. All these results enable to solve problems of image formation and reconstruction related to three Compton scattering tomography modalities.In addition we propose to improve models and algorithms es
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Wildman, Raymond A. "Geometry optimization and computational electromagnetics methods and applications /." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 191 p, 2008. http://proquest.umi.com/pqdweb?did=1481670101&sid=23&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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Books on the topic "Inverse Scattering Transform"

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S, Couchman L., ed. Inverse problems and inverse scattering of plane waves. San Diego, Calif: Academic, 2002.

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Solitons in multidimensions: Inverse spectral transform method. Singapore: World Scientific, 1993.

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1945-, Deift Percy, and Tomei Carlos, eds. Direct and inverse scattering on the line. Providence, R.I: American Mathematical Society, 1988.

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Colton, David L. Inverse acoustic and electromagnetic scattering theory. 2nd ed. New York: Springer, 1998.

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L, Colton David. Inverse acoustic and elctromagnetic scattering theory. 2nd ed. New York: Springer, 1997.

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L, Colton David. Inverse acoustic and electromagnetic scattering theory. Berlin: Springer-Verlag, 1992.

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Hopcraft, K. I. An introduction to electromagnetic inverse scattering. Dordrecht: Springer, 1992.

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Ablowitz, Mark J. Solitons, nonlinear evolution equations and inverse scattering. Cambridge: Cambridge University Press, 1991.

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Bona, Jerry, Roy Choudhury, and David Kaup, eds. The Legacy of the Inverse Scattering Transform in Applied Mathematics. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/conm/301.

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Ablowitz, Mark J. Solitons, nonlinear evolution equations and inverse scattering. Cambridge: Cambridge University Press, 1991.

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Book chapters on the topic "Inverse Scattering Transform"

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Maimistov, A. I., and A. M. Basharov. "Inverse Scattering Transform Method." In Nonlinear Optical Waves, 107–32. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-2448-7_3.

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Kravchenko, Vladislav V. "Inverse Scattering Transform Method." In Direct and Inverse Sturm-Liouville Problems, 29–31. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47849-0_7.

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Kaup, D. J. "Approximations for the Inverse Scattering Transform." In Dynamical Problems in Soliton Systems, 12–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02449-2_3.

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Debnath, Lokenath. "Solitons and the Inverse Scattering Transform." In Nonlinear Partial Differential Equations for Scientists and Engineers, 331–404. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4899-2846-7_9.

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Debnath, Lokenath. "Solitons and the Inverse Scattering Transform." In Nonlinear Partial Differential Equations for Scientists and Engineers, 425–533. Boston: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8265-1_9.

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Aktosun, Tuncay. "Inverse Scattering Transform, KdV, and Solitons." In Current Trends in Operator Theory and its Applications, 1–22. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7881-4_1.

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Beals, R., P. Deift, and X. Zhou. "The Inverse Scattering Transform on the Line." In Springer Series in Nonlinear Dynamics, 7–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58045-1_2.

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Aktosun, Tuncay. "Inverse Scattering Transform and the Theory of Solitons." In Encyclopedia of Complexity and Systems Science, 1–21. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-3-642-27737-5_295-3.

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Aktosun, Tuncay. "Inverse Scattering Transform and the Theory of Solitons." In Mathematics of Complexity and Dynamical Systems, 771–82. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_47.

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Aktosun, Tuncay. "Inverse Scattering Transform and the Theory of Solitons." In Encyclopedia of Complexity and Systems Science, 4960–71. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-30440-3_295.

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Conference papers on the topic "Inverse Scattering Transform"

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Roy, D. N. Ghosh, and D. V. G. L. N. Rao. "INVERSE SCATTERING TRANSFORM IN STIMULATED LIGHT SCATTERING." In A Volume in Honor of the 70th Birthday of Nicolaas Bloembergen. WORLD SCIENTIFIC, 1990. http://dx.doi.org/10.1142/9789814540223_0011.

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Nijhof, J. H. B., S. K. Turitsyn, and N. J. Doran. "Dispersion-managed solitons and the inverse scattering transform." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: OSA, 1999. http://dx.doi.org/10.1364/nlgw.1999.thd18.

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Gelash, A. A., R. I. Mullyadzhanov, and L. L. Frumin. "Direct and inverse scattering transform algorithm for complex wave fields." In Международный семинар по волоконным лазерам. ИАиЭ СО РАН, 2020. http://dx.doi.org/10.31868/rfl2020.28.

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Ablowitz, M., B. Fuchssteiner, and M. Kruskal. "Topics in Soliton Theory and Exactly Solvable Nonlinear Equations." In Conference on Nonlinear Evolution Equations, Solitons and the Inverse Scattering Transform. WORLD SCIENTIFIC, 1987. http://dx.doi.org/10.1142/9789814542210.

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Xinyu, Zhang, Shi Aiguo, Cai Feng, Xi Wentao, and Yu Huiyuan. "Nonlinear information analysis of ocean waves based on inverse scattering transform." In 2017 4th International Conference on Information, Cybernetics and Computational Social Systems (ICCSS). IEEE, 2017. http://dx.doi.org/10.1109/iccss.2017.8091453.

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Vitanov, Nikolay K. "Simple equations method (SEsM) and its connection with the inverse scattering transform method." In SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040409.

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Ho, Derek S., Sanghoon Kim, Tyler Drake, and Adam Wax. "Wavelet Transform Based Fast Inverse Light Scattering Analysis for Size Determination of Spherical Scatterers." In Biomedical Optics. Washington, D.C.: OSA, 2014. http://dx.doi.org/10.1364/biomed.2014.bs3a.50.

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Zhang, Sheng, and Xudong Gao. "A New Variable-Coefficient AKNS Hierarchy and its Exact Solutions via Inverse Scattering transform." In 2016 4th International Conference on Machinery, Materials and Information Technology Applications. Paris, France: Atlantis Press, 2016. http://dx.doi.org/10.2991/icmmita-16.2016.228.

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Mohtat, Ali, Solomon C. Yim, Nasim Adami, and Pedro Lomonaco. "A General Nonlinear Wavemaker Theory for Intermediate- to Deep-Water Waves Using Inverse Scattering Transform." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-19359.

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Abstract Analysis and generation of (nonlinear) intermediate- to deep-water waves with large steepness in experimental facilities are some of the most challenging tasks in wave mechanics. The inherent instability of water waves in deep-water waves makes the linear-based wave generation and analysis less accurate and incapable of generating and characterizing correctly nonlinear behavior of the target wave field. In this presented research, a detailed assessment of the wavemaker theories and steps included in experimental approaches are presented. After establishing the nonlinear behavior of generated intermediate- to deep-water waves, a novel wavemaker theory based on the nonlinear Schrödinger equation is proposed. The implementation of the proposed wavemaker theory shows its capability of generating deep-water waves more accurately and preserving the correct order of nonlinearity.
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Zeroug, Smaine, and Leopold B. Felsen. "Windowed-Transform Processing of Acoustic Beam Scattering From Fluid-Immersed Elastic Structures." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0422.

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Abstract Acoustic beam scattering from submerged bulk and layered elastic structures is of interest for applications ranging from determining material properties to locating and identifying interior defects. Nonspecular reflection, which occurs when the incident beam is phase matched to leaky waves (LW) supported by the structure, constitutes an effective sensor for such applications. Forward frequency domain modeling based on a robust asymptotic hybrid beam-LW algorithm [Zeroug and Felsen, 1992] has shown that the nonspecular data, which is established by interference between specular reflection and LWs, depends strongly on the collimation of the incident beam, the number and leakage strengths of the excited LWs, and the curvature of the insonified structure. The present contribution addresses the inverse problem of extracting this phenomenology via wave-oriented processing, which is implemented by subjecting the scattered field data to a Gaussian-windowed Fourier transform (GWT) along spatial tracks parallel to the fluid-structure interface. For the fluid-immersed elastic configurations of: 1) solid half-spaces, 2) plates, 3) solid cylinders, and 4) cylindrical shells, the GWT-generated local wavenumber phase-space distributions footprint the correct wave physics, but with resolutions that are limited by the configuration-spectrum tradeoff. Examples demonstrate how the resolution is influenced by the GWT window size. The paper also includes preliminary results on application of a Prony superresolution algorithm for extraction of LW phase velocities and leakage rates.
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Reports on the topic "Inverse Scattering Transform"

1

Kaup, D. J., and Y. Matsuno. On the Inverse Scattering Transform for the Benjamin-Ono Equation,. Fort Belvoir, VA: Defense Technical Information Center, January 1997. http://dx.doi.org/10.21236/ada342473.

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