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Geometric Theory Of Non Linear Differential Equations
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Book Synopsis Geometrical Methods in the Theory of Ordinary Differential Equations by : V.I. Arnold
Download or read book Geometrical Methods in the Theory of Ordinary Differential Equations written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.
Book Synopsis Geometric Function Theory and Non-linear Analysis by : Tadeusz Iwaniec
Download or read book Geometric Function Theory and Non-linear Analysis written by Tadeusz Iwaniec and published by Clarendon Press. This book was released on 2001 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.
Book Synopsis Differential Equations by : Solomon Lefschetz
Download or read book Differential Equations written by Solomon Lefschetz and published by . This book was released on 1977 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geared toward upper-level undergraduates and graduate students, this text investigates nonlinear differential equations of the second order and includes an extensive overview of the classical literature. 1957 edition.
Book Synopsis Geometric Theory of Semilinear Parabolic Equations by : Daniel Henry
Download or read book Geometric Theory of Semilinear Parabolic Equations written by Daniel Henry and published by Springer. This book was released on 2006-11-15 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Analysis of Nonlinear Partial Differential Equations by : Valentin Lychagin
Download or read book Geometric Analysis of Nonlinear Partial Differential Equations written by Valentin Lychagin and published by MDPI. This book was released on 2021-09-03 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.
Book Synopsis Geometric Analysis and Nonlinear Partial Differential Equations by : Stefan Hildebrandt
Download or read book Geometric Analysis and Nonlinear Partial Differential Equations written by Stefan Hildebrandt and published by Springer Science & Business Media. This book was released on 2003 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature. Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.
Book Synopsis Geometric Structures in Nonlinear Physics by : Robert Hermann
Download or read book Geometric Structures in Nonlinear Physics written by Robert Hermann and published by Math Science Press. This book was released on 1991 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.
Book Synopsis Nonlinear PDEs, Their Geometry, and Applications by : Radosław A. Kycia
Download or read book Nonlinear PDEs, Their Geometry, and Applications written by Radosław A. Kycia and published by Springer. This book was released on 2019-05-18 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents lectures given at the Summer School Wisła 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wisła, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Ampère equations. Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.
Book Synopsis Nonlinear partial differential equations in differential geometry by : Robert Hardt
Download or read book Nonlinear partial differential equations in differential geometry written by Robert Hardt and published by American Mathematical Soc.. This book was released on 1996 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Book Synopsis Geometric and Algebraic Structures in Differential Equations by : P.H. Kersten
Download or read book Geometric and Algebraic Structures in Differential Equations written by P.H. Kersten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
Book Synopsis Geometric Analysis of Nonlinear Partial Differential Equations by : Valentin Lychagin
Download or read book Geometric Analysis of Nonlinear Partial Differential Equations written by Valentin Lychagin and published by . This book was released on 2021 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a collection of twelve papers that reflect the state of the art of nonlinear differential equations in modern geometrical theory. It comprises miscellaneous topics of the local and nonlocal geometry of differential equations and the applications of the corresponding methods in hydrodynamics, symplectic geometry, optimal investment theory, etc. The contents will be useful for all the readers whose professional interests are related to nonlinear PDEs and differential geometry, both in theoretical and applied aspects.
Book Synopsis Contact Geometry and Nonlinear Differential Equations by : Alexei Kushner
Download or read book Contact Geometry and Nonlinear Differential Equations written by Alexei Kushner and published by Cambridge University Press. This book was released on 2007 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.
Book Synopsis Applications of Analytic and Geometric Methods to Nonlinear Differential Equations by : P.A. Clarkson
Download or read book Applications of Analytic and Geometric Methods to Nonlinear Differential Equations written by P.A. Clarkson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.
Book Synopsis Cartanian Geometry, Nonlinear Waves, and Control Theory by : Robert Hermann
Download or read book Cartanian Geometry, Nonlinear Waves, and Control Theory written by Robert Hermann and published by . This book was released on 1979 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convex Analysis and Nonlinear Geometric Elliptic Equations by : Ilya J. Bakelman
Download or read book Convex Analysis and Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.
Book Synopsis Differential Equations and Dynamical Systems by : Lawrence Perko
Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.
Book Synopsis Glimpses of Soliton Theory by : Alex Kasman
Download or read book Glimpses of Soliton Theory written by Alex Kasman and published by American Mathematical Society. This book was released on 2023-03-30 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book challenges and intrigues from beginning to end. It would be a treat to use for a capstone course or senior seminar. —William J. Satzer, MAA Reviews on Glimpses of Soliton Theory (First Edition) Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena like rogue waves and DNA transcription. Solitons of light are even used by engineers for data transmission and optical switches. Furthermore, unlike most nonlinear partial differential equations, soliton equations have the remarkable property of being exactly solvable. Explicit solutions to those equations provide a rare window into what is possible in the realm of nonlinearity. Glimpses of Soliton Theory reveals the hidden connections discovered over the last half-century that explain the existence of these mysterious mathematical objects. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra, the book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Hierarchy, and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make the subject accessible to undergraduates, numerous worked examples and thought-provoking exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of Mathematica® to facilitate computation and animate solutions. The second edition refines the exposition in every chapter, adds more homework exercises and projects, updates references, and includes new examples involving non-commutative integrable systems. Moreover, the chapter on KdV multisolitons has been greatly expanded with new theorems providing a thorough analysis of their behavior and decomposition.
