Introduction To Multidimensional Integrable Equations

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Introduction to Multidimensional Integrable Equations

Author : B.G. Konopelchenko
Publisher : Springer Science & Business Media
ISBN 13 : 1489911707
Total Pages : 298 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Introduction to Multidimensional Integrable Equations by : B.G. Konopelchenko

Download or read book Introduction to Multidimensional Integrable Equations written by B.G. Konopelchenko and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

Integrable Hamiltonian Hierarchies

Author : Vladimir Gerdjikov
Publisher : Springer Science & Business Media
ISBN 13 : 3540770534
Total Pages : 645 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Integrable Hamiltonian Hierarchies by : Vladimir Gerdjikov

Download or read book Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and published by Springer Science & Business Media. This book was released on 2008-06-02 with total page 645 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.

Introduction to Multidimensional Integrable Equations

Author : B. G. Konopelchenko
Publisher :
ISBN 13 : 9781489911711
Total Pages : 304 pages
Book Rating : 4.9/5 (117 download)

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Book Synopsis Introduction to Multidimensional Integrable Equations by : B. G. Konopelchenko

Download or read book Introduction to Multidimensional Integrable Equations written by B. G. Konopelchenko and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Continuous Symmetries and Integrability of Discrete Equations

Author : Decio Levi
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
ISBN 13 : 0821843540
Total Pages : 520 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Continuous Symmetries and Integrability of Discrete Equations by : Decio Levi

Download or read book Continuous Symmetries and Integrability of Discrete Equations written by Decio Levi and published by American Mathematical Society, Centre de Recherches Mathématiques. This book was released on 2023-01-23 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Quantum Theory, Deformation and Integrability

Author : R. Carroll
Publisher : Elsevier
ISBN 13 : 0080540082
Total Pages : 421 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Quantum Theory, Deformation and Integrability by : R. Carroll

Download or read book Quantum Theory, Deformation and Integrability written by R. Carroll and published by Elsevier. This book was released on 2000-11-09 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.

SIDE III -- Symmetries and Integrability of Difference Equations

Author : D. Levi
Publisher : American Mathematical Soc.
ISBN 13 : 0821821288
Total Pages : 462 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis SIDE III -- Symmetries and Integrability of Difference Equations by : D. Levi

Download or read book SIDE III -- Symmetries and Integrability of Difference Equations written by D. Levi and published by American Mathematical Soc.. This book was released on 2000 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the third meeting on "Symmetries and Integrability of Difference Equations" (SIDE III). The collection includes original results not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art. Research in the field of difference equations-often referred to more generally as discrete systems-has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete Painlevé equations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems. The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.

KdV ’95

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401100179
Total Pages : 507 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis KdV ’95 by : Michiel Hazewinkel

Download or read book KdV ’95 written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exactly one hundred years ago, in 1895, G. de Vries, under the supervision of D. J. Korteweg, defended his thesis on what is now known as the Korteweg-de Vries Equation. They published a joint paper in 1895 in the Philosophical Magazine, entitled `On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary wave', and, for the next 60 years or so, no other relevant work seemed to have been done. In the 1960s, however, research on this and related equations exploded. There are now some 3100 papers in mathematics and physics that contain a mention of the phrase `Korteweg-de Vries equation' in their title or abstract, and there are thousands more in other areas, such as biology, chemistry, electronics, geology, oceanology, meteorology, etc. And, of course, the KdV equation is only one of what are now called (Liouville) completely integrable systems. The KdV and its relatives continually turn up in situations when one wishes to incorporate nonlinear and dispersive effects into wave-type phenomena. This centenary provides a unique occasion to survey as many different aspects of the KdV and related equations. The KdV equation has depth, subtlety, and a breadth of applications that make it a rarity deserving special attention and exposition.

Waveguide Propagation of Nonlinear Waves

Author : Sergey Leble
Publisher : Springer
ISBN 13 : 3030226522
Total Pages : 298 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Waveguide Propagation of Nonlinear Waves by : Sergey Leble

Download or read book Waveguide Propagation of Nonlinear Waves written by Sergey Leble and published by Springer. This book was released on 2019-07-03 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions. Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.

New Technical Books

Author : New York Public Library
Publisher :
ISBN 13 :
Total Pages : 322 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis New Technical Books by : New York Public Library

Download or read book New Technical Books written by New York Public Library and published by . This book was released on 1993 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:

BETWEEN INSTINCT AND REASON

Author : DAVID SANDUA
Publisher : David Sandua
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4./5 ( download)

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Book Synopsis BETWEEN INSTINCT AND REASON by : DAVID SANDUA

Download or read book BETWEEN INSTINCT AND REASON written by DAVID SANDUA and published by David Sandua. This book was released on 2024-05-03 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an in-depth exploration of fear, examining its crucial role from the dawn of humanity to modernity. It reveals how fear, beyond being a simple instinctive defence mechanism, has acted as a catalyst for cultural, social and technological development throughout history. The book investigates the biological roots of fear and its role in the fight or flight response, showing how this primitive instinct continues to influence our reactions to threats today. By delving into historical cases and psychological perspectives, the book illustrates how fear has shaped decisions and behaviour, highlighting its impact on public policy and personal relationships. It also offers strategies for transforming fear from an overwhelming paralysis to a motivating force for innovation and personal growth. With an accessible and scientifically rigorous approach, this book is essential for those interested in understanding and redirecting one of the most powerful and pervasive emotions of our species towards human well-being and progress.

Solitons In Multidimensions: Inverse Spectral Transform Method

Author : B G Konopelchenko
Publisher : World Scientific
ISBN 13 : 9814518069
Total Pages : 304 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Solitons In Multidimensions: Inverse Spectral Transform Method by : B G Konopelchenko

Download or read book Solitons In Multidimensions: Inverse Spectral Transform Method written by B G Konopelchenko and published by World Scientific. This book was released on 1993-04-30 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.

Scattering, Two-Volume Set

Author : E. R. Pike
Publisher : Elsevier
ISBN 13 : 0080540732
Total Pages : 1831 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Scattering, Two-Volume Set by : E. R. Pike

Download or read book Scattering, Two-Volume Set written by E. R. Pike and published by Elsevier. This book was released on 2001-10-09 with total page 1831 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scattering is the collision of two objects that results in a change of trajectory and energy. For example, in particle physics, such as electrons, photons, or neutrons are "scattered off" of a target specimen, resulting in a different energy and direction. In the field of electromagnetism, scattering is the random diffusion of electromagnetic radiation from air masses is an aid in the long-range sending of radio signals over geographic obstacles such as mountains. This type of scattering, applied to the field of acoustics, is the spreading of sound in many directions due to irregularities in the transmission medium. Volume I of Scattering will be devoted to basic theoretical ideas, approximation methods, numerical techniques and mathematical modeling. Volume II will be concerned with basic experimental techniques, technological practices, and comparisons with relevant theoretical work including seismology, medical applications, meteorological phenomena and astronomy. This reference will be used by researchers and graduate students in physics, applied physics, biophysics, chemical physics, medical physics, acoustics, geosciences, optics, mathematics, and engineering. This is the first encyclopedic-range work on the topic of scattering theory in quantum mechanics, elastodynamics, acoustics, and electromagnetics. It serves as a comprehensive interdisciplinary presentation of scattering and inverse scattering theory and applications in a wide range of scientific fields, with an emphasis, and details, up-to-date developments. Scattering also places an emphasis on the problems that are still in active current research. The first interdisciplinary reference source on scattering to gather all world expertise in this technique Covers the major aspects of scattering in a common language, helping to widening the knowledge of researchers across disciplines The list of editors, associate editors and contributors reads like an international Who's Who in the interdisciplinary field of scattering

Differential Equations, Mathematical Modeling and Computational Algorithms

Author : Vladimir Vasilyev
Publisher : Springer Nature
ISBN 13 : 3031285050
Total Pages : 294 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Differential Equations, Mathematical Modeling and Computational Algorithms by : Vladimir Vasilyev

Download or read book Differential Equations, Mathematical Modeling and Computational Algorithms written by Vladimir Vasilyev and published by Springer Nature. This book was released on 2023-06-06 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Geometric Methods in Physics XL

Author : Piotr Kielanowski
Publisher : Springer Nature
ISBN 13 : 3031624076
Total Pages : 466 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Geometric Methods in Physics XL by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XL written by Piotr Kielanowski and published by Springer Nature. This book was released on 2024 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include: Yang-Baxter equation The restricted Siegel disc and restricted Grassmannian Geometric and deformation quantization Degenerate integrability Lie algebroids and groupoids Skew braces Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas

Cosmology and Gravitation II

Author : Marius Paul Bernard Novella
Publisher : Atlantica Séguier Frontières
ISBN 13 : 9782863321928
Total Pages : 596 pages
Book Rating : 4.3/5 (219 download)

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Book Synopsis Cosmology and Gravitation II by : Marius Paul Bernard Novella

Download or read book Cosmology and Gravitation II written by Marius Paul Bernard Novella and published by Atlantica Séguier Frontières. This book was released on 1996 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 940 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integrability of Nonlinear Systems

Author : Yvette Kosmann-Schwarzbach
Publisher : Springer Science & Business Media
ISBN 13 : 9783540206309
Total Pages : 358 pages
Book Rating : 4.2/5 (63 download)

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Book Synopsis Integrability of Nonlinear Systems by : Yvette Kosmann-Schwarzbach

Download or read book Integrability of Nonlinear Systems written by Yvette Kosmann-Schwarzbach and published by Springer Science & Business Media. This book was released on 2004-02-17 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.