Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models

Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models

Author: Fritz Gesztesy

Publisher: Cambridge University Press

Published: 2003-06-05

Total Pages: 522

ISBN-13: 9781139439411

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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.


Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Author: Fritz Gesztesy

Publisher: Cambridge University Press

Published: 2008-09-04

Total Pages: 438

ISBN-13: 1139473778

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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.


Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Author: Fritz Gesztesy

Publisher: Cambridge University Press

Published: 2008-09-04

Total Pages: 0

ISBN-13: 9780521753081

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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.


Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models

Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models

Author: Fritz Gesztesy

Publisher: Cambridge University Press

Published: 2003-06-05

Total Pages: 518

ISBN-13: 9780521753074

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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).


Glimpses of Soliton Theory

Glimpses of Soliton Theory

Author: Alex Kasman

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 322

ISBN-13: 0821852450

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Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. --


Methods of Spectral Analysis in Mathematical Physics

Methods of Spectral Analysis in Mathematical Physics

Author: Jan Janas

Publisher: Springer Science & Business Media

Published: 2008-12-16

Total Pages: 437

ISBN-13: 3764387556

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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.


Geometric Methods in Physics XXXVIII

Geometric Methods in Physics XXXVIII

Author: Piotr Kielanowski

Publisher: Springer Nature

Published: 2020-10-27

Total Pages: 373

ISBN-13: 3030533050

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The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics. For the past eight years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities. The chapter “Toeplitz Extensions in Noncommutative Topology and Mathematical Physics” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.


Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Soliton Equations and Their Algebro-Geometric Solutions: Volume 2, (1+1)-Dimensional Discrete Models

Author: Fritz Gesztesy

Publisher: Cambridge University Press

Published: 2003

Total Pages: 0

ISBN-13: 0521753082

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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.