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BL
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| Record Number
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860438
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Conference of Mathematical Physics(2017 :, Grozny, Russia)
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| Title & Author
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Recent developments in integrable systems and related topics of mathematical physics : : Kezenoi-Am, Russia 2016 /\ Victor M. Buchstaber, Sotiris Konstantinou-Rizos, Alexander V. Mikhailov, editors.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2018]
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| Series Statement
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Springer proceedings in mathematics and statistics ;; volume 273
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| Page. NO
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1 online resource
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| ISBN
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3030048071
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: 9783030048075
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9783030048068
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| Notes
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2.1 Argument Shift on a Manifold
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| Contents
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Intro; Preface; Contents; Contributors; Acronyms; Introduction; Numerical Instability of the Akhmediev Breather and a Finite-Gap Model of It; 1 Introduction; 2 A Short Summary of Finite Gap Results; 3 The Numerical Instability of the Akhmediev Breather; 4 Numerical Experiments; 4.1 Effect of the Time Step; 4.2 Effect of Round-Off Errors; 4.3 Effect of the Cauchy Data; 4.4 Effect of the x-Grid Size; 5 Conclusions; References; Movable Poles of Painlevé I Transcendents and Singularities of Monodromy Data Manifolds; 1 Introduction; 2 Poles Parametrization in General Case
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2.2 Sklyanin Elliptic and Poisson Algebras2.3 Algebra Qn(Y,); 3 q5,k(Y)-Poisson Tensors; 3.1 Why n=5?; 3.2 H-Invariancy; 4 Cremona Transformation; 4.1 Generalities about Cremona Transformations; 4.2 Case n=4. Cremona transformation and Elliptic Curves.; 4.3 Quadro-Cubic Cremona Transformations; 4.4 A Remark on the Compatibility; 5 Klein and Moore Syzygies and Poisson Structures; 5.1 Klein Syzygy and Free Resolution Complex.; 5.2 Poisson Structure on P4 from Syzygies; 5.3 Moore Syzygies and Corresponding 3-Folds.; 5.4 Poisson Structure on P4 from Moore Syzygies
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3 Group Law and New Integrable Systems on the Plane3.1 Hénon-Heiles System; 3.2 System with Quartic Potential; 4 Equivalence Relations and New Integrable Systems on the Plane; 4.1 Separation of Variables and Abel Differential Equation; 4.2 Construction of the New Integrable System on T*R; 4.3 Other New Integrable Systems on the Plane; 5 Conclusion; References; Quadro-Cubic Cremona Transformations and Feigin-Odesskii-Sklyanin Algebras with 5 Generators; 1 Introduction; 2 Poisson Algebras and Elliptic Poisson Algebras; 2.1 Poisson Algebras on Affine Varieties
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3 Singularities of the Monodromy Manifold P14 Truncated Solutions of PI Equation; 4.1 1-Truncated Solutions; 4.2 2-Truncated Solutions; 5 Formation of Truncated Solutions; References; Elliptic Calogero-Moser Hamiltonians and Compatible Poisson Brackets; 1 Introduction; 2 Polynomial Forms for Elliptic Quantum Calogero-Moser Hamiltonians; 3 Classical Case; 4 Conclusion; References; Bäcklund Transformations and New Integrable Systems on the Plane; 1 Introduction; 2 Divisor Arithmetic on Hyperelliptic Curves; 2.1 Some Explicit Formulae for Arithmetic on Genus 2 Hyperelliptic Curves
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5.5 ``Quantum'' Cremona TransformationsReferences; From Reflection Equation Algebra to Braided Yangians; 1 Introduction; 2 Braidings: Definitions and Properties; 3 Braided Lie Algebras and their Affinization; 4 Characteristic Polynomials for Generating Matrices; 5 Braided Yangians; 6 Shifted Braided q-Yangian and its q=1 Limit; References; Survey of the Deformation Quantization of Commutative Families; 1 Introduction; 1.1 The Main Question; 1.2 Argument Shift Method and Enveloping Algebras; 1.3 Presentation and Organization of the Text; 2 The Argument Shift Method and Nijenhuis Operators
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| Abstract
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This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.--
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| Subject
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Mathematical physics, Congresses.
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| Subject
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Mathematical physics.
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| Dewey Classification
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530.15
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| LC Classification
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QC19.2.C66 2017
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| Added Entry
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Buchstaber, V. M.
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Konstantinou-Rizos, Sotiris
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Mikhailov, Alexander V.,1953-
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