Inverse Problems And Nonlinear Evolution Equations

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Inverse Problems And Nonlinear Evolution Equations

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Author : Alexander L. Sakhnovich
language : en
Publisher: Walter de Gruyter
Release Date : 2013-07-31

Inverse Problems And Nonlinear Evolution Equations written by Alexander L. Sakhnovich and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-31 with Mathematics categories.

This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

Inverse Problems For Kinetic And Other Evolution Equations

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Author : I︠U︡riĭ Evgenʹevich Anikonov
language : en
Publisher: VSP
Release Date : 2001

Inverse Problems For Kinetic And Other Evolution Equations written by I︠U︡riĭ Evgenʹevich Anikonov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

This monograph in the "Inverse and Ill-Posed Problems Series deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements.A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.This monograph will be of value and interest to mathematicians, engineers and other specialists dealing with inverse and ill posed problems.

Inverse Problems For Kinetic And Other Evolution Equations

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Author : Yu. E. Anikonov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-07-24

Inverse Problems For Kinetic And Other Evolution Equations written by Yu. E. Anikonov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.

This monograph deals with methods of studying multidimensional inverse problems for kinetic and other evolution equations, in particular transfer equations. The methods used are applied to concrete inverse problems, especially multidimensional inverse problems applicable in linear and nonlinear statements. A significant part of the book contains formulas and relations for solving inverse problems, including formulas for the solution and coefficients of kinetic equations, differential-difference equations, nonlinear evolution equations, and second order equations.

Solitons Nonlinear Evolution Equations And Inverse Scattering

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Author : Mark J. Ablowitz
language : en
Publisher: Cambridge University Press
Release Date : 1991-12-12

Solitons Nonlinear Evolution Equations And Inverse Scattering written by Mark J. Ablowitz 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 1991-12-12 with Mathematics categories.

This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The Workshop Needs 91

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Author : M Boiti
language : en
Publisher: World Scientific
Release Date : 1992-08-26

Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The Workshop Needs 91 written by M Boiti and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-26 with categories.

The Workshop NEEDS '91 brought together, from all over the world, scientists engaged in research on nonlinear systems, either their underlying mathematical properties or their physical applications. Accordingly, many talks were devoted to present methods of solution (like spectral transform) and to the investigation of structural (geometrical and/or algebraic) properties of (continuous and discrete) nonlinear evolution equations. Peculiar nonlinear systems, such as cellular automata, were also discussed. Applications to various fields of physics, namely, quantum field theory, fluid dynamics, general relativity and plasma physics were considered.

Nonlinear Evolution Equations

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Author : Nina B. Maslova
language : en
Publisher: World Scientific
Release Date : 1993

Nonlinear Evolution Equations written by Nina B. Maslova and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.

Nonlinear Evolution Equations And Painleve Test

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Author : N Euler
language : en
Publisher: World Scientific
Release Date : 1988-10-01

Nonlinear Evolution Equations And Painleve Test written by N Euler and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10-01 with Mathematics categories.

This book is an edited version of lectures given by the authors at a seminar at the Rand Afrikaans University. It gives a survey on the Painlevé test, Painlevé property and integrability. Both ordinary differential equations and partial differential equations are considered.

Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The 8th International Workshop Needs 92

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Author : Vladimir G Makhankov
language : en
Publisher: World Scientific
Release Date : 1993-08-13

Nonlinear Evolution Equations And Dynamical Systems Proceedings Of The 8th International Workshop Needs 92 written by Vladimir G Makhankov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-08-13 with categories.

NEEDs '92 was held in Dubna, Russia in July 1992. This set of proceedings compiles the lectures and short contributions on the soliton theory and its applications presented during the conference. The topics covered included the most recent results on relevant problems of nonlinear evolution systems such as: Multidimensional Integrable Systems, Geometric and Algebraic Methods, Painleve Property, Lie-Backlund Symmetries, Spectral Methods, Solitons and Coherent Structures, Computational Methods, Quantum Field and String Theories, Nonlinear Optics and Hydrodynamics, Condensed Matter etc. The extent of coverage for these important topics makes this book useful, informative and insighful for the mathematics and theoretical physics community, both the senior researches and those just entering the field.

Backlund Transformations

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Author :
language : en
Publisher:
Release Date : 1976

Backlund Transformations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Contact transformations categories.

Formulas In Inverse And Ill Posed Problems

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Author : IU. IUrii Evgenevich Anikonov
language : en
Publisher: VSP
Release Date : 1997-01-01

Formulas In Inverse And Ill Posed Problems written by IU. IUrii Evgenevich Anikonov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.