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Dissertations / Theses on the topic 'Inverse method'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Li, Xi. "Focused inverse method for LF." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18796.

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Logical frameworks allow us to specify formal systems and prove properties about them. One interesting logical framework is Twelf, a language that uses higher order abstract syntax to encode object languages into the meta language. Currently, uniform proofs have been used for describing proof search in backwards logic programming style. However, there are certain limitations to a backward system, for example, loop-detection mechanisms are required for some of the simplest problems to yield a solution. As a consequence, the search for a more effective proof search algorithm prevails and a forwa

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2

Deolmi, Giulia. "Computational Parabolic Inverse Problems." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.

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This thesis presents a general approach to solve numerically parabolic Inverse Problems, whose underlying mathematical model is discretized using the Finite Element method. The proposed solution is based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problem of pollution rate estimation.<br>In questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo

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3

Lin, Lianshan. "Characterization of material properties using inverse method." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.505378.

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The inverse analysis introduced in this dissertation involves detennining an object's properties. In engineering problems, the most important object properties are material or constitutive constants (elastic/plastic). In direct problems, engineers can conveniently look up for the material constants in standard materials handbooks, and use them to pred'ict the structure's responses under the given loads. However, in the cases where the material constants are not available from standard handbooks, or the material properties need to be detennined precisely since a small difference from those list

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4

QUEIROZ, MARCIO SANTOS DE. "INVERSE DYNAMICS METHOD FOR ROBOT MANIPULATOR CONTROL." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 1993. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=19548@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>O método da dinâmica inversa para o controle de manipuladores robóticos é apresentado. A ideia básica deste método é cancelar as não linearidades e acoplamentos, que caracterizam o comportamento dinâmico de manipuladores, através de um modelo dinâmico do mesmo (controlador primário). Com isto, o sistema resultante é linear e desaclopado, podendo ser controlado por técnicas de controle linear (controlador secundário). O método é inicialmente desenvolvido considerando o caso ideal do controlador primário (onde o modelo dinâmico é p

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5

Butler, Samuel Thomas James. "Inverse Scattering Transform Method for Lattice Equations." Thesis, The University of Sydney, 2012. http://hdl.handle.net/2123/8724.

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The main original contribution of this thesis is the development of a fully discrete inverse scattering transform (IST) method for nonlinear partial difference equations. The equations we solve are nonlinear partial difference equations on a quad-graph, also called lattice equations, which are known to be multidimensionally consistent in N dimensions for arbitrary N. Such equations were discovered by Nijhoff, Quispel and Capel and Adler and later classified by Adler, Bobenko and Suris. The main equation solved by our IST framework is the Q3δ lattice equation. Our approach also solves all of it

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6

Skare, Steven Edward. "An Inverse Design Method for Supersonic Airfoils." DigitalCommons@CalPoly, 2012. https://digitalcommons.calpoly.edu/theses/731.

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Airfoil design is one of the most important aspects of aircraft design. Slight changes in airfoil geometry can lead to significant changes in a wide variety of aircraft performance metrics. Inverse design methods offer an efficient alternative to standard direct methods. The key to this design problem is to derive a direct relationship between changes in airfoil geometry and changes in pressure or velocity distributions. This relationship is then used to modify an initial airfoil and its pressure distribution to match a target pressure distribution, which is specified by design parameters.

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7

Castellet, Llerena Albert. "Solving inverse kinematics problems using an interval method." Doctoral thesis, Universitat Politècnica de Catalunya, 1998. http://hdl.handle.net/10803/5936.

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de la tesi<br/><br/>El principal objectiu d'aquesta tesi és establir una base teòrica que permeti resoldre problemes cinemàtics inversos mitjançant mètodes d'intervals.<br/><br/>La primera part de la tesi desenvolupa i formalitza una nova metodologia per a l'anàlisi de cadenes cinemàtiques espacials. Aquest enfoc es basa en l'estudi de la varietat d'automoviment del mecanisme esfèric ortogonal i en la seva relació amb el mecanisme de n-barres. El principal avantatge respecte a altres mètodes és la seva senzillesa i sobretot la seva generalitat, que permet el mateix tractament del problema per

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8

Hazarika, Neep. "An inverse method for blended wing-body configurations." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/12498.

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9

Figueiredo, Patric. "Iterative method for solving inverse heat conduction problems." Master's thesis, Universidade de Aveiro, 2014. http://hdl.handle.net/10773/14400.

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10

Kang, Sangwoo. "Direct sampling method in inverse electromagnetic scattering problem." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS417/document.

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Le problème de l'imagerie non itérative dans le cadre de la diffraction électromagnétique inverse utilisant la méthode d'échantillonnage direct (DSM) est considéré. Grâce à une combinaison de l'expression asymptotique du champ proche ou du champ lointain diffracté et de l'hypothèse de petits obstacles, les expressions analytiques de la fonction d'indicateur DSM sont présentées dans diverses configurations telles que des configurations 2D/3D, mono-/multi-configurations statiques, à vue limitée/complète et fréquence unique/ diversité en fréquence. Une fois l'expression analytique obtenue, sa str

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11

Maree, A. J. "The inverse finite element method : sensitivity to measurement setup /." Link to the online version, 2005. http://hdl.handle.net/10019/1088.

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12

Silieti, Mahmood. "INVERSE BOUNDARY ELEMENT/GENETIC ALGORITHM METHOD FOR RECONSTRUCTION O." Doctoral diss., University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3325.

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A methodology is formulated for the solution of the inverse problem concerned with the reconstruction of multi-dimensional heat fluxes for film cooling applications. The motivation for this study is the characterization of complex thermal conditions in industrial applications such as those encountered in film cooled turbomachinery components. The heat conduction problem in the metal endwall/shroud is solved using the boundary element method (bem), and the inverse problem is solved using a genetic algorithm (ga). Thermal conditions are overspecified at exposed surfaces amenable to measurement,

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13

Mellings, Sharon Christine. "Flaw identification using the inverse dual boundary element method." Thesis, University of Portsmouth, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239881.

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14

Maree, Abraham Jacobus. "The Inverse Finite Element Method: Sensitivity to Measurement Setup." Thesis, Stellenbosch : University of Stellenbosch, 2005. http://hdl.handle.net/10019.1/2640.

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Thesis (MScEng (Civil Engineering))--University of Stellenbosch, 2005.<br>In the inverse finite element method (iFEM), given a finite element model of a structure and imperfect displacement measurements, the external loads acting on the structure can be assessed. The basic idea behind iFEM is the optimization of a quadratic cost function of the difference between the measured and estimated values, with a high cost corresponding to a high precision of the measurements. In the present research it is firstly shown how the iFEM theory was broadened to accommodate for strain measurements thro

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15

Hazanee, Areena. "Boundary element method for solving inverse heat source problems." Thesis, University of Leeds, 2015. http://etheses.whiterose.ac.uk/10570/.

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In this thesis, the boundary element method (BEM) is applied for solving inverse source problems for the heat equation. Through the employment of the Green’s formula and fundamental solution, the BEM naturally reduces the dimensionality of the problem by one although domain integrals are still present due to the initial condition and the heat source. We mainly consider the identification of time-dependent source for heat equation with several types of conditions such as non-local, non-classical, periodic, fixed point, time-average and integral which are considered as boundary or overdeterminat

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16

Ross, Christopher Roger. "Direct and inverse scattering by rough surfaces." Thesis, Brunel University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318675.

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17

Zhang, Wenlong. "Forward and Inverse Problems Under Uncertainty." Thesis, Paris Sciences et Lettres (ComUE), 2017. http://www.theses.fr/2017PSLEE024/document.

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Cette thèse contient deux matières différentes. Dans la première partie, deux cas sont considérés. L'un est le modèle plus lisse de la plaque mince et l'autre est les équations des limites elliptiques avec des données limites incertaines. Dans cette partie, les convergences stochastiques des méthodes des éléments finis sont prouvées pour chaque problème.Dans la deuxième partie, nous fournissons une analyse mathématique du problème inverse linéarisé dans la tomographie d'impédance électrique multifréquence. Nous présentons un cadre mathématique et numérique pour une procédure d'imagerie du tens

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18

Bircan, Ali. "Solution Of Inverse Electrocardiography Problem Using Minimum Relative Entropy Method." Master's thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612574/index.pdf.

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The interpretation of heart&#039<br>s electrical activity is very important in clinical medicine since contraction of cardiac muscles is initiated by the electrical activity of the heart. The electrocardiogram (ECG) is a diagnostic tool that measures and records the electrical activity of the heart. The conventional 12 lead ECG is a clinical tool that provides information about the heart status. However, it has limited information about functionality of heart due to limited number of recordings. A better alternative approach for understanding cardiac electrical activity is the incorporation of

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19

Rahmati, M. T. "Incompressible Navier-Stokes inverse design method based on unstructured meshes." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1445805/.

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Two inverse methods for turbomachinery blade design are developed. In these inverse design approaches blade shapes are computed for a specified design parameter such as mass-averaged tangential velocity or pressure loading distribution. These inverse methods directly define a geometry needed to obtain these prescribed target design parameters which are related to the performance of turbomachinery blades. The first method is based on the prescription of pressure loading on the blade while the second method is based on the prescription of mass-averaged tangential velocity on the blade. In both m

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20

Li, Hong. "An inverse reliability method and its applications in engineering design." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0026/NQ38929.pdf.

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21

Zhong, Ming. "Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems." Thesis, University of Maryland, College Park, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128674.

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<p> We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedne

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22

Shinde, Krushna. "Interval uncertainty method to treat inconsistent measurements in inverse problems." Thesis, Compiègne, 2021. http://www.theses.fr/2021COMP2594.

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Le problème inverse consiste à trouver les valeurs des paramètres d’un modèle physique à partir d’un ensemble de mesures. Dans les problèmes de génie mécanique, la caractérisation du comportement des matériaux nécessite une méthode inverse pour identifier les paramètres des matériaux. Le problème d’identification déterministe est généralement sensible aux données, et une façon de résoudre ce problème est de prendre en compte les incertitudes dans les données. Bien que plusieurs de ces méthodes existent dans la littérature, la plupart d’entre elles utilisent la minimisation des moindres carrés

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23

Sztefek, Pavel. "Inverse method for stiffness determination of impact damage in composites." Thesis, Imperial College London, 2009. http://hdl.handle.net/10044/1/5556.

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The limited knowledge of stiffness reductions is a major problem in reliably predicting the post-impact strength of composite structures. This work describes development and application of a non-destructive approach for evaluation of the inplane stiffness of impact damage in composites. The approach combines an inverse method linked to a finite element model and non-contact full-field measurements. The material parameters of impact damage are determined by iteratively matching the finite element model to displacement fields measured optically during post-impact loading. A first order, gradient

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24

Frassek, Rouven. "Q-operators, Yangian invariance and the quantum inverse scattering method." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2014. http://dx.doi.org/10.18452/17070.

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Inspiriert von den integrablen Strukturen der schwach gekoppelten planaren N=4 Super-Yang-Mills-Theorie studieren wir Q-Operatoren und Yangsche Invarianten. Wir geben eine Übersicht der Quanten-Inverse-Streumethode zusammen mit der Yang-Baxter Gleichung welche zentral für diesen systematischen Zugang zu integrablen Modellen ist. Den Fokus richten wir auf rationale integrable Spinketten und Vertexmodelle. Wir besprechen einige ihrer bekannten Gemeinsamkeiten und wie sie durch Bethe-Ansatz-Methoden mit Hilfe sogenannter Q-Funktionen gelöst werden können. Der Hauptteil basiert auf den ursprünglic

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25

Djedidi, Mouad. "Design of a Fast Antenna Characterization Method Exploiting Echoes." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS348/document.

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Les techniques de mesure de diagramme de rayonnement d’antenne actuelles partagent un paradigme commun qui stipule que l’information utile est exclusivement portée par le signal de test généré. Cela implique un effort mécanique fastidieux en faisant tourner l'antenne sous test ou en déplaçant le système de sondes afin de couvrir des angles de mesure différents jusqu'à ce qu'une caractérisation complète soit effectuée ; une limitation qui est généralement surmontée en utilisant des systèmes multisondes coûteux. En outre, toute réflexion provenant du site de mesure et des équipements de test est

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26

Ismatullah. "Analysis of space-borne antennas by higher-order method of moments and inverse equivalent current methods." kostenfrei, 2010. https://mediatum2.ub.tum.de/node?id=977261.

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27

Nightingale, Miriam. "Material Characterization of Cardiovascular Biomaterials Using an Inverse Finite Element Method." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/36426.

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Being able to accurately model soft tissue behaviour, such as that of heart valvular tissue, is essential for developing effective numerical simulations of in-vivo conditions and determining patient-specific care options. Although several analytical material models, based on strain energy functions, have been successful in predicting soft tissue behaviour, complications arise when these models are implemented into finite element (FE) programs due to the incorporation of a penalty parameter for numerically enforcing material incompressibility. Specifically, material parameters determined throug

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28

Santos, Luis Carlos de Castro. "A hybrid inverse optimization method for aerodynamic design of lifting surfaces." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/12105.

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29

Yla-Maihaniemi, Pirre Paivikki. "A novel method for investigating solid-liquid interactions : inverse liquid chromatography." Thesis, Imperial College London, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429885.

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30

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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31

Farcas, Adrian. "The dual reciprocity boundary element method for solving some inverse problems." Thesis, University of Leeds, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411306.

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32

Reeve, Thomas Henry. "The method of fundamental solutions for some direct and inverse problems." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4278/.

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We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require

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33

Brock, Jerry S. "A consistent direct-iterative inverse design method for the Euler equations." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40033.

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A new, consistent direct-iterative method is proposed for the solution of the aerodynamic inverse design problem. Direct-iterative methods couple analysis and shape modification methods to iteratively determine the geometry required to support a target surface pressure. The proposed method includes a consistent shape modification method wherein the identical governing equations are used in both portions of the design procedure. The new shape modification method is simple, having been developed from a truncated, quasi-analytical Taylor's series expansion of the global governing equations. This

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34

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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35

Eser, Hülya Tıhmınlıoğlu Funda. "Diffusion And Equilibrium Measurements In Polymer-Solvent Systems By Inverse Gas Chromatography Method/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/kimya/T000451.pdf.

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36

Li, Xiaobei. "Instrumentation and inverse problem solving for impedance imaging /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/5973.

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37

Borges, Carlos. "A multifrequency method for the solution of the acoustic inverse scattering problem." Digital WPI, 2013. https://digitalcommons.wpi.edu/etd-dissertations/12.

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We are interested in solving the time-harmonic inverse acoustic scattering problem for planar sound-soft obstacles. In this work, we introduce four methods for solving inverse scattering problems. The first method is a variation of the method introduced by Johansson and Sleeman. This method solves the inverse problem when we have the far field pattern given for only one incident wave. It is an iterative method based on a pair of integral equations used to obtain the far field pattern of a known single object. The method proposed in this thesis has a better computational performance than the me

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38

Helin, Mikael. "Inverse Parameter Estimation using Hamilton-Jacobi Equations." Thesis, KTH, Numerisk analys, NA, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123092.

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Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possibl

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39

Alqadah, Hatim F. "Space-Frequency Regularization for Qualitative Inverse Scattering." University of Cincinnati / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1321967202.

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40

André, Etienne. "An inverse method for the synthesis of timing parameters in concurrent systems." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2010. http://tel.archives-ouvertes.fr/tel-00595268.

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This thesis proposes a novel approach for the synthesis of delays for timed systems, in particular in the framework oftimed automata, a model for verifying real-time systems. Our approach relies on the following inverse method: given a reference valuation of the parameters, we synthesize a constraint on the parameters, guaranteeing the same timeabstract linear behavior as for the reference valuation. This gives a criterion of robustness to the system. By iterating this inverse method on various points of a bounded parameter domain, we are then able to partition the parametric space into good a

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Yeh, T. C. Jim, and Jinqi Zhang. "A Geostatistical Inverse Method for Variably Saturated Flow in the Vadose Zone." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1995. http://hdl.handle.net/10150/614185.

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A geostatistical inverse technique utilizing both primary and secondary information is developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated hydraulic conductivity and pore -size distribution parameters) in the vadose zone. Measurements of saturated hydraulic conductivity and pore -size distribution parameters are considered as the primary information, while measurements of steady -state flow processes (soil -water pressure head and degree of saturation) are regarded as the secondary information. This inverse approach relies on the classical

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Zhang, Jinqi, and T. C. Jim Yeh. "An Iterative Geostatistical Inverse Method For Steady-Flow In The Vadose Zone." Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1996. http://hdl.handle.net/10150/614010.

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An iterative stochastic inverse technique utilizing both primary and secondary information is developed to estimate conditional means of unsaturated hydraulic conductivity parameters (saturated hydraulic conductivity and pore -size distribution parameters) in the vadose zone. Measurements of saturated hydraulic conductivity and pore -size distribution parameter are considered as the primary information, while measurements of steady -state flow processes (soil -water pressure head and degree of saturation) are regarded as the secondary information. This inverse approach is similar to the

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43

De, Villiers Jean Schepers. "Inverse method in seismology." Thesis, 2009. http://hdl.handle.net/10500/3784.

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The problem of fitting a material property of the earth to a certain model by analysing a returned seismic signal is investigated here. Analysis proceeds with methods taken from the theory of inverse problems. Seismic wave inversion is tack- led by minimisation of the objective function with respect to the model parameters. Absorbing boundary conditions are implemented using an exponentially decaying ansatz.<br>Physics<br>Ph. D. (Physics)

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44

Abdel-Khalik, Hany Samy. "Inverse method applied to adaptive core simulation." 2002. http://www.lib.ncsu.edu/theses/available/etd-11042002-114525/unrestricted/etd.pdf.

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45

Erhard, Klaus. "Point Source Approximation Methods in Inverse Obstacle Reconstruction Problems." Doctoral thesis, 2005. http://hdl.handle.net/11858/00-1735-0000-0006-B402-4.

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"Solving inverse kinematics problems using an interval method." Universitat Politècnica de Catalunya, 1998. http://www.tesisenxarxa.net/TDX-0723102-153600/.

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47

Picado, de Carvalho Serranho Pedro Miguel. "A Hybrid Method for Inverse Obstacle Scattering Problems." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B38F-0.

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48

Chang, Mei-Hsia, and 張美霞. "Development and Applications of Inverse Heat Transfer Method." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/02625416116501744718.

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博士<br>大同大學<br>機械工程學系(所)<br>93<br>The aim of this thesis is to develop inverse heat transfer methods and apply these methods to optimal design problems in different areas. The inverse heat transfer methods developed in the present thesis include the conjugate-gradient method (CGM), simplified conjugate-gradient method (SCGM), and automatic-filter scheme (AFS). Firstly, the CGM method is modified and categorized into two types: polynomial-function approach and point-by-point approach to extend its feasibility in (1) shape identification for the ice layer within the cylindrical capsules in cold s

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Wang, Chun-Jen, and 王俊仁. "Study of optimal fin shape by inverse method." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/86793749140171160903.

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碩士<br>逢甲大學<br>機械工程學所<br>96<br>The inverse heat transfer method was adopted in this research to study the optimal three-dimensional fin shape profile of a finned-tube heat exchanger. A modified conjugate gradient method was developed in this research, the method could succeed in obtaining the optimal three-dimensional fin shape profile. The effects of different fin materials and flow velocities were studied with dimensional form;and the effects of different Biot number distributions were also studied with dimensionless form in this research. It is observed by the numerical results that the fin

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LIN, QIONG-XIAN, and 林瓊仙. "Korteweg-de Vries Equation and Inverse Scattering Method." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/67242767137255095259.

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碩士<br>淡江大學<br>數學研究所<br>80<br>1834年J.Scott Russell 在愛丁堡的格拉斯哥運河，觀察到一種奇妙的水波，稱之為“孤立波”。其後的數十年間，科學家們並未能在流體運動中找出形容此種奇特現象的運動方程式。 1895年，Korteweg 和de Vries 建立單向運動的淺水波運動方程 ˍ η 3 ／g 1 2 1 η ─── ＝ ─ ／ ─ ── （ ─η＋ ─αη＋ ─ σ ─── ）ｔ 2 ＼／ l x 2 3 3 x 即 Korteweg - de Vries 方程，簡稱Kdv 方程。令人感興趣的是這個方程具有孤立波解，因此我們在理論上證實了孤立波的存在。此後，科學家們則在不同領域中也導出Kdv 方程。

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