A Dressing Method In Mathematical Physics

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A Dressing Method In Mathematical Physics

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Author : Evgeny V. Doktorov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-19

A Dressing Method In Mathematical Physics written by Evgeny V. Doktorov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-19 with Science categories.

This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.

Nonlinear Waves A Geometrical Approach

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Author : Angela Slavova
language : en
Publisher: World Scientific Publishing
Release Date : 2018-11-16

Nonlinear Waves A Geometrical Approach written by Angela Slavova and has been published by World Scientific Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-16 with Mathematics categories.

This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg-Whitham equation, Vakhnenko equation, Camassa-Holm equation, several versions of the NLS equation, Kaup-Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.Readers not familiar with the complicated methods used in the theory of the equations of mathematical physics (functional analysis, harmonic analysis, spectral theory, topological methods, a priori estimates, conservation laws) can easily be acquainted here with different solutions of some nonlinear PDEs written in a sharp form (waves), with their geometrical visualization and their interpretation. In many cases, explicit solutions (waves) having specific physical interpretation (solitons, kinks, peakons, ovals, loops, rogue waves) are found and their interactions are studied and geometrically visualized. To do this, classical methods coming from the theory of ordinary differential equations, the dressing method, Hirota's direct method and the method of the simplest equation are introduced and applied. At the end, the paradifferential approach is used.This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

Methods Of Mathematical Physics

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Author : Harold Jeffreys
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-18

Methods Of Mathematical Physics written by Harold Jeffreys and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-18 with Mathematics categories.

This book is a reissue of classic textbook of mathematical methods.

Methods For Solving Mathematical Physics Problems

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Author : Valeriĭ Ivanovich Agoshkov
language : en
Publisher: Cambridge Int Science Publishing
Release Date : 2006

Methods For Solving Mathematical Physics Problems written by Valeriĭ Ivanovich Agoshkov and has been published by Cambridge Int Science Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.

The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.

Mathematical Methods In Physics And Engineering

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Author : John W. Dettman
language : en
Publisher: Courier Corporation
Release Date : 2013-01-23

Mathematical Methods In Physics And Engineering written by John W. Dettman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-23 with Science categories.

Intended for college-level physics, engineering, or mathematics students, this volume offers an algebraically based approach to various topics in applied math. It is accessible to undergraduates with a good course in calculus which includes infinite series and uniform convergence. Exercises follow each chapter to test the student's grasp of the material; however, the author has also included exercises that extend the results to new situations and lay the groundwork for new concepts to be introduced later. A list of references for further reading will be found at the end of each chapter. For this second revised edition, Professor Dettman included a new section on generalized functions to help explain the use of the Dirac delta function in connection with Green's functions. In addition, a new approach to series solutions of ordinary differential equations has made the treatment independent of complex variable theory. This means that the first six chapters can be grasped without prior knowledge of complex variables. However, since Chapter 8 depends heavily on analytic functions of a complex variable, a new Chapter 7 on analytic function theory has been written.

Mathematical Methods For Physicists And Engineers

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Author : Royal Eugene Collins
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11

Mathematical Methods For Physicists And Engineers written by Royal Eugene Collins and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Science categories.

Practical text focuses on fundamental applied math needed to deal with physics and engineering problems: elementary vector calculus, special functions of mathematical physics, calculus of variations, much more. 1968 edition.

Mathematical Methods Using Mathematica

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Author : Sadri Hassani
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-10

Mathematical Methods Using Mathematica written by Sadri Hassani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-10 with Science categories.

Intended as a companion for textbooks in mathematical methods for science and engineering, this book presents a large number of numerical topics and exercises together with discussions of methods for solving such problems using Mathematica(R). Although it is primarily designed for use with the author's "Mathematical Methods: For Students of Physics and Related Fields," the discussions in the book sufficiently self-contained that the book can be used as a supplement to any of the standard textbooks in mathematical methods for undergraduate students of physical sciences or engineering.

Selected Mathematical Methods In Theoretical Physics

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Author : Vladmir P. Krainov
language : en
Publisher: CRC Press
Release Date : 2001-10-18

Selected Mathematical Methods In Theoretical Physics written by Vladmir P. Krainov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-18 with Science categories.

Selected Mathematical Methods in Theoretical Physics shows how a scientist, knowing the answer to a problem intuitively or through experiment, can develop a mathematical method to prove that answer. The approach adopted by the author first involves the formulation of differential or integral equations for describing the physical procession, the basis of more general physical laws. Then the approximate solution of these equations is worked out, using small dimensionless physical parameters, or using numerical parameters for the objects under consideration. The eleven chapters of the book, which can be read in sequence or studied independently of each other, contain many examples of simple physical models, as well as problems for students to solve. This is a supplementary textbook for advanced university students in theoretical physics. It will enrich the knowledge of students who already have a solid grounding in mathematical analysis.

Mathematical Methods In Physics

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Author : Samuel D Lindenbaum
language : en
Publisher: World Scientific
Release Date : 1996-09-30

Mathematical Methods In Physics written by Samuel D Lindenbaum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-30 with Science categories.

This new book on Mathematical Methods In Physics is intended to be used for a 2-semester course for first year MA or PhD physics graduate students, or senior undergraduates majoring in physics, engineering or other technically related fields.Emphasis has been placed on physics applications, included where appropriate, to complement basic theories. Applications include moment of inertia in “Tensor Analysis”; Maxwell's equations, magnetostatic, stress tensor, continuity equation and heat flow in “fields”; special and spherical harmonics in “Hilbert Space”; electrostatics, hydrodynamics and Gamma function in “Complex Variable Theory”; vibrating string, vibrating membrane and harmonic oscillator in “Ordinary Differential Equations”; age of the earth and temperature variation of the earth's surface in “Heat Conduction”; and field due to a moving point charge (Liénard-Wiechart potentials) in “Wave Equations”.Subject not usually found in standard mathematical physics texts include Theory of Curves in Space in “Vector Analysis”, and Retarded and Advanced D-Functions in “Wave Equations”.Lastly, problem solving techniques are presented by way of appendices, comprising 75 pages of problems with their solutions. These problems provide applications as well as extensions to the theory.A useful compendium, with such excellent features, will surely make it a key reference text.

Mathematical Methods For Physicists

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Author : George B. Arfken
language : en
Publisher: Academic Press
Release Date : 2013-10-22

Mathematical Methods For Physicists written by George B. Arfken and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.

This new and completely revised Fourth Edition provides thorough coverage of the important mathematics needed for upper-division and graduate study in physics and engineering. Following more than 28 years of successful class-testing, Mathematical Methods for Physicists is considered the standard text on the subject. A new chapter on nonlinear methods and chaos is included, as are revisions of the differential equations and complex variables chapters. The entire book has been made even more accessible, with special attention given to clarity, completeness, and physical motivation. It is an excellent reference apart from its course use. This revised Fourth Edition includes: Modernized terminology Group theoretic methods brought together and expanded in a new chapter An entirely new chapter on nonlinear mathematical physics Significant revisions of the differential equations and complex variables chapters Many new or improved exercises Forty new or improved figures An update of computational techniques for today's contemporary tools, such as microcomputers, Numerical Recipes, and Mathematica(r), among others