Solitons And The Inverse Scattering Transform

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Solitons And The Inverse Scattering Transform

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Author : Mark J. Ablowitz
language : en
Publisher: SIAM
Release Date : 1981-01-01

Solitons And The Inverse Scattering Transform written by Mark J. Ablowitz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localized pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. For such exactly solvable problems, the inverse scattering transform provides the general solution of their initial value problems. It is equally surprising that some of these exactly solvable problems arise naturally as models of physical phenomena. Simply put, the inverse scattering transform is a nonlinear analog of the Fourier transform used for linear problems. Its value lies in the fact that it allows certain nonlinear problems to be treated by what are essentially linear methods. Chapters 1 and 2 of the book describe in detail the theory of the inverse scattering transform. Chapter 3 discusses alternate methods for these exactly solvable problems and the interconnections among them. Physical applications are described in Chapter 4, where, for example, similarities between deep water waves and nonlinear optics become evident. Because of the fundamental role of linear theory, there is an extensive appendix that addresses the linear problems and their solutions.

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.

B Cklund Transformations The Inverse Scattering Method Solitons And Their Applications

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Author : Robert M. Miura
language : en
Publisher: Springer
Release Date : 2006-11-14

B Cklund Transformations The Inverse Scattering Method Solitons And Their Applications written by Robert M. Miura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974

Solitons And The Inverse Scattering Transform

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Author : Mark J. Ablowitz
language : en
Publisher: SIAM
Release Date : 2006-05-15

Solitons And The Inverse Scattering Transform written by Mark J. Ablowitz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-15 with Mathematics categories.

A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Theory Of Solitons

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Author : S. Novikov
language : en
Publisher: Springer Science & Business Media
Release Date : 1984-05-31

Theory Of Solitons written by S. Novikov 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 1984-05-31 with Mathematics categories.

The Inverse Scattering Transformation And The Theory Of Solitons

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Author : W. Eckhaus
language : en
Publisher: Elsevier
Release Date : 2011-08-18

The Inverse Scattering Transformation And The Theory Of Solitons written by W. Eckhaus and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

The Inverse Scattering Transformation and The Theory of Solitons

Solitons

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Author : P. G. Drazin
language : en
Publisher: Cambridge University Press
Release Date : 1989-02-09

Solitons written by P. G. Drazin 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 1989-02-09 with Mathematics categories.

This textbook is an introduction to the theory of solitons in the physical sciences.

Direct And Inverse Sturm Liouville Problems

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Author : Vladislav V. Kravchenko
language : en
Publisher: Birkhäuser
Release Date : 2020-08-18

Direct And Inverse Sturm Liouville Problems written by Vladislav V. Kravchenko and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-18 with Mathematics categories.

This book provides an introduction to the most recent developments in the theory and practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A universal approach for practical solving of direct and inverse spectral and scattering problems is presented, based on the notion of transmutation (transformation) operators and their efficient construction. Analytical representations for solutions of Sturm-Liouville equations as well as for the integral kernels of the transmutation operators are derived in the form of functional series revealing interesting special features and lending themselves to direct and simple numerical solution of a wide variety of problems. The book is written for undergraduate and graduate students, as well as for mathematicians, physicists and engineers interested in direct and inverse spectral problems.

Introduction To Multidimensional Integrable Equations

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Author : B.G. Konopelchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Introduction To Multidimensional Integrable Equations written by B.G. Konopelchenko 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 2013-06-29 with Science categories.

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.