Soliton Equations And Their Algebro Geometric Solutions Volume I 1 1 Dimensional Continuous Models

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 9780521753081
Total Pages : 0 pages
Book Rating : 4.82/5 ( download)

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Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2008-09-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a partner to Volume 1: Dimensional Continuous Models, this book provides a self-contained introduction to solition equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices.

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 1139473778
Total Pages : 438 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2008-09-04 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

Author : Fritz Gesztesy
Publisher :
ISBN 13 : 9780521753074
Total Pages : 518 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models written by Fritz Gesztesy and published by . This book was released on 2003-06-05 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a detailed treatment of a class of algebro-geometric solutions and their representations.

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 0521753082
Total Pages : 0 pages
Book Rating : 4.81/5 ( download)

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Download or read book Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results.

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 9780521753074
Total Pages : 0 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2003-06-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions; also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary and time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces).

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 9781139439411
Total Pages : 522 pages
Book Rating : 4.13/5 ( download)

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Download or read book Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2003-06-05 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces). The presentation is rigorous, detailed, and self-contained, with ample background material provided in various appendices. Detailed notes for each chapter together with an exhaustive bibliography enhance the presentation offered in the main text.

Author : Fritz Gesztesy
Publisher : Cambridge University Press
ISBN 13 : 9780521753074
Total Pages : 518 pages
Book Rating : 4.74/5 ( download)

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Download or read book Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models written by Fritz Gesztesy and published by Cambridge University Press. This book was released on 2003-06-05 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions; also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive treatment of the class of algebro-geometric solutions in the stationary and time-dependent contexts is provided. The formalism presented includes trace formulas, Dubrovin-type initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses techniques from the theory of differential equations, spectral analysis, and elements of algebraic geometry (most notably, the theory of compact Riemann surfaces).

Author : Fritz Gesztesy
Publisher :
ISBN 13 : 9780511427664
Total Pages : 438 pages
Book Rating : 4.62/5 ( download)

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Download or read book Soliton Equations and Their Algebro-geometric Solutions written by Fritz Gesztesy and published by . This book was released on 2008 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions.

Author : Jan Janas
Publisher : Springer Science & Business Media
ISBN 13 : 3764387556
Total Pages : 437 pages
Book Rating : 4.56/5 ( download)

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Download or read book Methods of Spectral Analysis in Mathematical Physics written by Jan Janas and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.

Author : Boling Guo
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110470578
Total Pages : 211 pages
Book Rating : 4.74/5 ( download)

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Download or read book Rogue Waves written by Boling Guo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-06-26 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of the theoretical research on rogue waves and discusses solutions to rogue wave formation via the Darboux and bilinear transformations, algebro-geometric reduction, and inverse scattering and similarity transformations. Studies on nonlinear optics are included, making the book a comprehensive reference for researchers in applied mathematics, optical physics, geophysics, and ocean engineering. Contents The Research Process for Rogue Waves Construction of Rogue Wave Solution by the Generalized Darboux Transformation Construction of Rogue Wave Solution by Hirota Bilinear Method, Algebro-geometric Approach and Inverse Scattering Method The Rogue Wave Solution and Parameters Managing in Nonautonomous Physical Model