Solitons and the Inverse Scattering Transform (Studies in Applied and Numerical Mathematics) - Softcover

Ablowitz, Mark J.; Segur, Harvey

9780898714777: Solitons and the Inverse Scattering Transform (Studies in Applied and Numerical Mathematics)

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ISBN 10: 089871477X ISBN 13: 9780898714777

Verlag: CAMBRIDGE, 1981

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A study of the inverse scattering transform and its application to problems of nonlinear dispersive waves.

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Verlag: CAMBRIDGE
Erscheinungsdatum: 1981
Sprache: Englisch
ISBN 10: 089871477X
ISBN 13: 9780898714777
Einband: Taschenbuch
Anzahl der Seiten: 435
Kontakt zum Hersteller: Nicht verf�gbar
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Solitons and Inverse Scattering Transform (SIAM Studies in Applied Mathematics, No. 4)

Ablowitz, Mark J.; Segur, Harvey

Verlag: Society for Industrial and Applied Mathematics, 2000

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Solitons and the Inverse Scattering Transform (eng)

Ablowitz, Mark J.

Verlag: Society for Industrial and Applied Mathematics, 2000

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Solitons and the Inverse Scattering Transform

Ablowitz, Mark J./ Segur, Harvey

Verlag: Society for Industrial & Applied, 2006

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Solitons and the Inverse Scattering Transform

Ablowitz, Mark J.; Segur, Harvey

Verlag: Society for Industrial & Applied Mathematics,U.S., 2000

ISBN 10: 089871477X ISBN 13: 9780898714777

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Solitons and the Inverse Scattering Transform

M. Ablowitz, H. Segur

Verlag: Society for Industrial and Applied Mathematics,U.S., US, 2006

ISBN 10: 089871477X ISBN 13: 9780898714777

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Paperback. Zustand: New. 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. Bestandsnummer des Verk�ufers LU-9780898714777

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Solitons and the Inverse Scattering Transform (Paperback)

M. Ablowitz

Verlag: Society for Industrial & Applied Mathematics,U.S., New York, 2006

ISBN 10: 089871477X ISBN 13: 9780898714777

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Paperback. Zustand: new. Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verk�ufers 9780898714777

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