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Author : B. G. Konopelchenko
Publisher :
ISBN 13 : 9781489911711
Total Pages : 304 pages
Book Rating : 4.9/5 (117 download)
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:
Author : B.G. Konopelchenko
Publisher : Springer Science & Business Media
ISBN 13 : 1489911707
Total Pages : 298 pages
Book Rating : 4.4/5 (899 download)
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.
Author : Gennadi Vainikko
Publisher : Springer
ISBN 13 : 354047773X
Total Pages : 169 pages
Book Rating : 4.5/5 (44 download)
Download or read book Multidimensional Weakly Singular Integral Equations written by Gennadi Vainikko and published by Springer. This book was released on 2006-11-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final aim of the book is to construct effective discretization methods to solve multidimensional weakly singular integral equations of the second kind on a region of Rn e.g. equations arising in the radiation transfer theory. To this end, the smoothness of the solution is examined proposing sharp estimates of the growth of the derivatives of the solution near the boundary G. The superconvergence effect of collocation methods at the collocation points is established. This is a book for graduate students and researchers in the fields of analysis, integral equations, mathematical physics and numerical methods. No special knowledge beyond standard undergraduate courses is assumed.
Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
ISBN 13 : 9491216171
Total Pages : 245 pages
Book Rating : 4.4/5 (912 download)
Download or read book Multidimensional Integral Equations and Inequalities written by B.G. Pachpatte and published by Springer Science & Business Media. This book was released on 2011-07-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.
Author : S. G. Mikhlin
Publisher : Elsevier
ISBN 13 : 1483164497
Total Pages : 172 pages
Book Rating : 4.4/5 (831 download)
Download or read book Multidimensional Singular Integrals and Integral Equations written by S. G. Mikhlin and published by Elsevier. This book was released on 2014-07-10 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.
Author : M. M. Lavrentiev
Publisher : Springer
ISBN 13 : 3540364048
Total Pages : 65 pages
Book Rating : 4.5/5 (43 download)
Download or read book Multidimensional Inverse Problems for Differential Equations written by M. M. Lavrentiev and published by Springer. This book was released on 2006-11-15 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir Gerdjikov
Publisher : Springer
ISBN 13 : 3540770542
Total Pages : 643 pages
Book Rating : 4.5/5 (47 download)
Download or read book Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and published by Springer. This book was released on 2008-12-02 with total page 643 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.
Author : Gennadi Vainikko
Publisher :
ISBN 13 : 9783662171592
Total Pages : 180 pages
Book Rating : 4.1/5 (715 download)
Download or read book Multidimensional Weakly Singular Integral Equations written by Gennadi Vainikko and published by . This book was released on 2014-01-15 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Carroll
Publisher : Elsevier
ISBN 13 : 9780080540085
Total Pages : 420 pages
Book Rating : 4.5/5 (4 download)
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 420 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.
Author : Solomon Grigorʹevich Mikhlin
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (642 download)
Download or read book Multidimensional Singular Integrals and Integral Equations written by Solomon Grigorʹevich Mikhlin and published by . This book was released on 1965 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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)
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.
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401100179
Total Pages : 507 pages
Book Rating : 4.4/5 (11 download)
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.
Author : J. Hietarinta
Publisher : Cambridge University Press
ISBN 13 : 1316654087
Total Pages : 461 pages
Book Rating : 4.3/5 (166 download)
Download or read book Discrete Systems and Integrability written by J. Hietarinta and published by Cambridge University Press. This book was released on 2016-08-19 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.
Author : Sergey Leble
Publisher : Springer
ISBN 13 : 3030226522
Total Pages : 288 pages
Book Rating : 4.0/5 (32 download)
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 288 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.
Author : DAVID SANDUA
Publisher : David Sandua
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4./5 ( download)
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.
Author : Decio Levi
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870211
Total Pages : 468 pages
Book Rating : 4.8/5 (72 download)
Download or read book SIDE III written by Decio Levi and published by American Mathematical Soc.. This book was released on 2000-06-15 with total page 468 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 Painleve 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.
Author :
Publisher : CRC Press
ISBN 13 : 9782881248399
Total Pages : 404 pages
Book Rating : 4.2/5 (483 download)
Download or read book Multidimensional Integral Transformations written by and published by CRC Press. This book was released on 1992 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cross between a textbook and a monograph, this extensive introduction discusses all of the most important transformations, compiling information otherwise scattered throughout the literature. Attention is concentrated on the operational calculus of the major integral transformations and some of its applications, with an investigation of transforms in spaces of functions and of distributions. Annotation copyrighted by Book News, Inc., Portland, OR
