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Books on the topic 'Nonlinear field equations'

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Published: 18 May 2024

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1

Benci, Vieri, and Donato Fortunato. Variational Methods in Nonlinear Field Equations. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06914-2.

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2

V, Murthy M. K., Spagnolo S, and Workshop on Nonlinear Hyperbolic Equations and Field Theory (1990 : Lake Como, Italy), eds. Nonlinear hyperbolic equations and field theory. Harlow, Essex, England: Longman Scientific & Technical, 1992.

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3

Selfdual gauge field vortices: An analytical approach. Boston, Mass: Birkhäuser, 2007.

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4

LeFloch, Philippe G. The hyperboloidal foliation method. New Jersey: World Scientific, 2015.

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5

Tarantello, Gabriella. Selfdual gauge field vortices: An analytical approach. Boston, Mass: Birkhäuser, 2007.

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6

Tarantello, Gabriella. Selfdual gauge field vortices: An analytical approach. Boston, Mass: Birkhäuser, 2007.

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7

Prikarpatskiĭ, A. K. Algebraicheskie aspekty integriruemosti nelineĭnykh dinamicheskikh sistem na mnogoobrazii͡a︡kh. Kiev: Nauk. dumka, 1991.

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8

Philippe, Blanchard, Dias J. P. 1944-, and Stubbe J. 1959-, eds. New methods and results in non-linear field equations: Proceedings of a conference held at the University of Bielefeld, Fed. Rep. of Germany, 7-10 July 1987. Berlin: Springer-Verlag, 1989.

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9

Korsunskiĭ, S. V. Nonlinear waves in dispersive and dissipative systems with coupled fields. Harlow, Essex: Longman, 1997.

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10

Gatica, Gabriel N. Boundary-field equation methods for a class of nonlinear problems. New York: Longman, 1995.

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11

Gatica, Gabriel N. Boundary-field equation methods for a class of nonlinear problems. New York: Longman, 1995.

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12

Gatica, Gabriel N. Boundary-field equation methods for a class of nonlinear problems. Harlow: Longman, 1995.

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13

1952-, Sanchez N., ed. Non-linear equations in classical and quantum field theory: Proceedings of a seminar series held at DAPHE, Observatoire de Meudon, and LPTHE, Université Pierre et Marie Curie, Paris, between October 1983 and October 1984. Berlin: Springer-Verlag, 1985.

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14

Guckenheimer, John. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. 2nd ed. New York: Springer-Verlag, 1986.

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15

Philip, Holmes, ed. Nonlinear oscillations, dynamical Systems and bifurcations of vector fields. Berlin: Springer, 1997.

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16

Guckenheimer, John. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. 5th ed. New York: Springer, 1997.

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17

Philip, Holmes, ed. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. 2nd ed. New York: Springer-Verlag, 1986.

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18

Guckenheimer, John. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. 3rd ed. New York: Springer-Verlag, 1990.

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19

Babeshko, Lyudmila, Mihail Bich, and Irina Orlova. Econometrics and econometric modeling. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1141216.

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The textbook covers a wide range of issues related to econometric modeling. Regression models are the core of econometric modeling, so the issues of their evaluation, testing of assumptions, adjustment and verification are given a significant place. Various aspects of multiple regression models are included: multicollinearity, dummy variables, and lag structure of variables. Methods of linearization and estimation of nonlinear models are considered. An apparatus for evaluating systems of simultaneous and apparently unrelated equations is presented. Attention is paid to time series models. Detailed solutions of the examples in Excel and the R software environment are included. Meets the requirements of the federal state educational standards of higher education of the latest generation. For undergraduate and graduate students studying in the field of "Economics", the curriculum of which includes the disciplines "Econometrics"," Econometric Modeling","Econometric research".

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20

Novikov, Anatoliy, Tat'yana Solodkaya, Aleksandr Lazerson, and Viktor Polyak. Econometric modeling in the GRETL package. ru: INFRA-M Academic Publishing LLC., 2023. http://dx.doi.org/10.12737/1732940.

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The tutorial describes the capabilities of the GRETL statistical package for computer data analysis and econometric modeling based on spatial data and time series. Using concrete economic examples, GRETL considers classical and generalized models of linear and nonlinear regression, methods for detecting and eliminating multicollinearity, models with variable structure, autoregressive processes, methods for testing and eliminating autocorrelation, as well as discrete choice models and systems of simultaneous equations. For the convenience of users, the tutorial contains all the task data files used in the work in the format .GDTs are collected in an application in the cloud so that users have access to them. Meets the requirements of the federal state educational standards of higher education of the latest generation in the disciplines of "Econometrics" and "Econometric modeling". For students and teachers of economic universities in the field of Economics, as well as researchers who use econometric methods to model socio-economic phenomena and processes.

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21

M, Greco Antonio, Ruggeri Tommaso, Boillat G, and Circolo matematico di Palermo, eds. Non linear hyperbolic fields and waves: A tribute to Guy Boillat. Palermo: Sede della Società, 2006.

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22

Steven, Rosenberg, and Clara L. Aldana. Analysis, geometry, and quantum field theory: International conference in honor of Steve Rosenberg's 60th birthday, September 26-30, 2011, Potsdam University, Potsdam, Germany. Providence, Rhode Island: American Mathematical Society, 2012.

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23

1957-, Gurvits Leonid, and Banff International Research Station for Mathematics Innovation & Discovery, eds. Randomization, relaxation, and complexity in polynomial equation solving: Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, February 28--March 5, 2010, Banff, Ontario [i.e. Alberta], Canada. Providence, R.I: American Mathematical Society, 2011.

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24

The endoscopic classification of representations orthogonal and symplectic groups. Providence, Rhode Island: American Mathematical Society, 2013.

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25

Harmonic maps and differential geometry: A harmonic map fest in honour of John C. Wood's 60th birthday, September 7-10, 2009, Cagliari, Italy. Providence, R.I: American Mathematical Society, 2011.

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26

ZnO bao mo zhi bei ji qi guang, dian xing neng yan jiu. Shanghai Shi: Shanghai da xue chu ban she, 2010.

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27

Murthy, M. K. V., and S. Spagnolo. Nonlinear Hyperbolic Equations and Field Theory. Taylor & Francis Group, 1992.

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28

Variational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and Vortices. Springer International Publishing AG, 2014.

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29

Benci, Vieri, and Donato Fortunato. Variational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and Vortices. Springer, 2014.

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30

Benci, Vieri, and Donato Fortunato. Variational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and Vortices. Springer, 2016.

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31

Tarantello, Gabriella. Self-Dual Gauge Field Vortices: An Analytical Approach (Progress in Nonlinear Differential Equations and Their Applications). Birkhäuser Boston, 2008.

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32

Deruelle, Nathalie, and Jean-Philippe Uzan. The Einstein equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0044.

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This chapter deals with Einstein equations. In the absence of matter there is no gravitational field, and the spacetime which represents this empty universe is Minkowski spacetime. More precisely, if the gravitational field created by the matter can be neglected, the appropriate framework for describing the matter is that of special relativity. Einstein gravitational equations relate geometry and matter: specifically, they relate the Riemann tensor, or more precisely the Einstein tensor, to the geometrical object describing ‘inertia’, the energy content of the matter—that is, the energy–momentum tensor. These equations form a set of ten nonlinear partial differential equations. The coordinate system can be chosen arbitrarily.

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33

Phase Optimizetion Problems. WILEY-VCH, 2010.

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34

Stubbe, Joachim, Joao-Paulo Dias, and Philippe Blanchard. New Methods and Results in Non-linear Field Equations: Proceedings of a Conference Held at the University of Bielefeld, Federal Republic of Germany, ... in Physics). Springer, 2014.

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35

Dias, J. P., and Philippe Blanchard. New Methods and Results in Non-Linear Field Equations: Proc of a Conference Held at the University of Bielefeld, Fed. Rep. of Germany, 7-10 July 198 (Lecture Notes in Physics). Springer, 1990.

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36

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.

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37

Christopher, Colin, Chengzhi Li, and Joan Torregrosa. Limit Cycles of Differential Equations. Springer International Publishing AG, 2022.

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38

Holmes, Philip, and John Guckenheimer. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer London, Limited, 2013.

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39

Holmes, Philip, and John Guckenheimer. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer New York, 2013.

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40

Zgurovsky, Mikhail Z., and Valery S. Melnik. Nonlinear Analysis and Control of Physical Processes and Fields. Springer Berlin / Heidelberg, 2012.

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41

Vislocky, Michael. Nonlinear stability analysis of an interfacial model equation for alloy solidification in the presence of an electric field. 1988.

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42

Guckenheimer, J., and P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Applied Mathematical Sciences). Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1990.

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43

Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston Ma. American Mathematical Society, 2013.

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44

Zgurovsky, Mikhail Z., and Valery S. Melnik. Nonlinear Analysis and Control of Physical Processes and Fields (Data and Knowledge in a Changing World). Springer, 2004.

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45

Limit Cycles of Differential Equations (Advanced Courses in Mathematics - CRM Barcelona). Birkhäuser Basel, 2007.

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46

Glazov, M. M. Dynamical Nuclear Polarization. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198807308.003.0005.

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The transfer of nonequilibrium spin polarization between the electron and nuclear subsystems is studied in detail. Usually, a thermal orientation of nuclei in magnetic field is negligible due to their small magnetic moments, but if electron spins are optically oriented, efficient nuclear spin polarization can occur. The microscopic approach to the dynamical nuclear polarization effect based on the kinetic equation method, along with a phenomenological but very powerful description of dynamical nuclear polarization in terms of the nuclear spin temperature concept is given. In this way, one can account for the interaction between neighbouring nuclei without solving a complex many-body problem. The hyperfine interaction also induces the feedback of polarized nuclei on the electron spin system giving rise to a number of nonlinear effects: bistability of nuclear spin polarization and anomalous Hanle effect, dragging and locking of optical resonances in quantum dots. Theory is illustrated by experimental data on dynamical nuclear polarization.

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