The Weierstrass Sigma Function In Higher Genus And Applications To Integrable Equations
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The Weierstrass Sigma Function In Higher Genus And Applications To Integrable Equations
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Author : Shigeki Matsutani
language : en
Publisher: Springer Nature
Release Date : 2025-03-25
The Weierstrass Sigma Function In Higher Genus And Applications To Integrable Equations written by Shigeki Matsutani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.
This book’s area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics. Special functions such as elliptic or automorphic functions have an algebro-geometric nature. These attributes permeate the book. The “Kleinian sigma function”, or “higher-genus Weierstrass sigma function” generalizes the elliptic sigma function. It appears for the first time in the work of Weierstrass. Klein gave an explicit definition for hyperelliptic or genus-three curves, as a modular invariant analogue of the Riemann theta function on the Jacobian (the two functions are equivalent). H.F. Baker later used generalized Legendre relations for meromorphic differentials, and brought out the two principles of the theory: on the one hand, sigma uniformizes the Jacobian so that its (logarithmic) derivatives in one direction generate the field of meromorphic functions on the Jacobian, therefore algebraic relations among them generate the ideal of the Jacobian as a projective variety; on the other hand, a set of nonlinear PDEs (which turns out to include the “integrable hierarchies” of KdV type), characterize sigma. We follow Baker’s approach. There is no book where the theory of the sigma function is taken from its origins up to the latest most general results achieved, which cover large classes of curves. The authors propose to produce such a book, and cover applications to integrable PDEs, and the inclusion of related al functions, which have not yet received comparable attention but have applications to defining specific subvarieties of the degenerating family of curves. One reason for the attention given to sigma is its relationship to Sato's tau function and the heat equations for deformation from monomial curves. The book is based on classical literature and contemporary research, in particular our contribution which covers a class of curves whose sigma had not been found explicitly before.
The Weierstrass Sigma Function In Higher Genus And Applications To Integrable Equations
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Author : Shigeki Matsutani
language : en
Publisher:
Release Date : 2025
The Weierstrass Sigma Function In Higher Genus And Applications To Integrable Equations written by Shigeki Matsutani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Geometry, Algebraic categories.
This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics. Special functions such as elliptic or automorphic functions have an algebro-geometric nature. These attributes permeate the book. The “Kleinian sigma function”, or “higher-genus Weierstrass sigma function” generalizes the elliptic sigma function. It appears for the first time in the work of Weierstrass. Klein gave an explicit definition for hyperelliptic or genus-three curves, as a modular invariant analogue of the Riemann theta function on the Jacobian (the two functions are equivalent). H.F. Baker later used generalized Legendre relations for meromorphic differentials, and brought out the two principles of the theory: on the one hand, sigma uniformizes the Jacobian so that its (logarithmic) derivatives in one direction generate the field of meromorphic functions on the Jacobian, therefore algebraic relations among them generate the ideal of the Jacobian as a projective variety; on the other hand, a set of nonlinear PDEs (which turns out to include the “integrable hierarchies” of KdV type), characterize sigma. We follow Baker's approach. There is no book where the theory of the sigma function is taken from its origins up to the latest most general results achieved, which cover large classes of curves. The authors propose to produce such a book, and cover applications to integrable PDEs, and the inclusion of related al functions, which have not yet received comparable attention but have applications to defining specific subvarieties of the degenerating family of curves. One reason for the attention given to sigma is its relationship to Sato's tau function and the heat equations for deformation from monomial curves. The book is based on classical literature and contemporary research, in particular our contribution which covers a class of curves whose sigma had not been found explicitly before.
Blow Up For Higher Order Parabolic Hyperbolic Dispersion And Schrodinger Equations
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Author : Victor A. Galaktionov
language : en
Publisher: CRC Press
Release Date : 2014-09-22
Blow Up For Higher Order Parabolic Hyperbolic Dispersion And Schrodinger Equations written by Victor A. Galaktionov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.
Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations shows how four types of higher-order nonlinear evolution partial differential equations (PDEs) have many commonalities through their special quasilinear degenerate representations. The authors present a unified approach to deal with these quasilinear PDEs.The book
Integrable Systems And Algebraic Geometry
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Author : Ron Donagi
language : en
Publisher: Cambridge University Press
Release Date : 2020-03-02
Integrable Systems And Algebraic Geometry written by Ron Donagi 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 2020-03-02 with Mathematics categories.
A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.
Geometric Methods In Physics Xxxv
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Author : Piotr Kielanowski
language : en
Publisher: Birkhäuser
Release Date : 2018-02-10
Geometric Methods In Physics Xxxv written by Piotr Kielanowski and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-10 with Mathematics categories.
This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. 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, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2003
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Nonlinear Waves
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Author : Lokenath Debnath
language : en
Publisher: CUP Archive
Release Date : 1983-12-30
Nonlinear Waves written by Lokenath Debnath and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-12-30 with Mathematics categories.
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
Separation Of Variables And Superintegrability
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Author : E. G. Kalnins
language : en
Publisher: IOP Publishing Limited
Release Date : 2018
Separation Of Variables And Superintegrability written by E. G. Kalnins and has been published by IOP Publishing Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Science categories.
Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting in a unified, updated and a more accessible manner the results scattered in the literature the authors have prepared an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.
Recurrence Sequences
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Author : Graham Everest
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Recurrence Sequences written by Graham Everest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
An Introduction To Random Matrices
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Author : Greg W. Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2010
An Introduction To Random Matrices written by Greg W. Anderson 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 2010 with Mathematics categories.
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.