Integrability, Quantization, and Geometry: I. Integrable Systems

Integrability, Quantization, and Geometry: I. Integrable Systems

Author: Sergey Novikov

Publisher: American Mathematical Soc.

Published: 2021-04-12

Total Pages: 516

ISBN-13: 1470455919

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This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.


Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry

Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry

Author: Sergey Novikov

Publisher: American Mathematical Soc.

Published: 2021-04-12

Total Pages: 480

ISBN-13: 1470455927

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This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.


Geometric Methods in Physics XL

Geometric Methods in Physics XL

Author: Piotr Kielanowski

Publisher: Springer Nature

Published: 2024

Total Pages: 466

ISBN-13: 3031624076

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Zusammenfassung: This volume collects papers based on lectures given at the XL Workshop on Geometric Methods in Physics, held in Białowieża, Poland in July 2023. These chapters provide readers an overview of cutting-edge research in infinite-dimensional groups, integrable systems, quantum groups, Lie algebras and their generalizations and a wide variety of other areas. Specific topics include: Yang-Baxter equation The restricted Siegel disc and restricted Grassmannian Geometric and deformation quantization Degenerate integrability Lie algebroids and groupoids Skew braces Geometric Methods in Physics XL will be a valuable resource for mathematicians and physicists interested in recent developments at the intersection of these areas


Nonlinear Science and Complexity

Nonlinear Science and Complexity

Author: J.A. Tenreiro Machado

Publisher: Springer Science & Business Media

Published: 2010-11-03

Total Pages: 411

ISBN-13: 9048198844

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This book contains selected papers of NSC08, the 2nd Conference on Nonlinear Science and Complexity, held 28-31 July, 2008, Porto, Portugal. It focuses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physics and mathematics. Topics treated include • Chaotic Dynamics and Transport in Classic and Quantum Systems • Complexity and Nonlinearity in Molecular Dynamics and Nano-Science • Complexity and Fractals in Nonlinear Biological Physics and Social Systems • Lie Group Analysis and Applications in Nonlinear Science • Nonlinear Hydrodynamics and Turbulence • Bifurcation and Stability in Nonlinear Dynamic Systems • Nonlinear Oscillations and Control with Applications • Celestial Physics and Deep Space Exploration • Nonlinear Mechanics and Nonlinear Structural Dynamics • Non-smooth Systems and Hybrid Systems • Fractional dynamical systems


Trends In Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of 9th International Workshop On Complex Structures, Integrability And Vector Fields

Trends In Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of 9th International Workshop On Complex Structures, Integrability And Vector Fields

Author: Stancho Dimiev

Publisher: World Scientific

Published: 2009-08-21

Total Pages: 290

ISBN-13: 9814467464

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This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa-Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.


Topics In Contemporary Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of The 8th International Workshop On Complex Structures And Vector Fields

Topics In Contemporary Differential Geometry, Complex Analysis And Mathematical Physics - Proceedings Of The 8th International Workshop On Complex Structures And Vector Fields

Author: Kouei Sekigawa

Publisher: World Scientific

Published: 2007-06-11

Total Pages: 350

ISBN-13: 9814475025

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This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.


Advanced Computing in Industrial Mathematics

Advanced Computing in Industrial Mathematics

Author: Ivan Georgiev

Publisher: Springer Nature

Published: 2021-04-03

Total Pages: 430

ISBN-13: 3030716163

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This book gathers the peer-reviewed proceedings of the 13th Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics, BGSIAM'18, held in Sofia, Bulgaria. The general theme of BGSIAM'18 was industrial and applied mathematics with particular focus on: mathematical physics, numerical analysis, high performance computing, optimization and control, mathematical biology, stochastic modeling, machine learning, digitization and imaging, advanced computing in environmental, biomedical and engineering applications.


Integrable Hamiltonian Hierarchies

Integrable Hamiltonian Hierarchies

Author: Vladimir Gerdjikov

Publisher: Springer

Published: 2008-12-02

Total Pages: 645

ISBN-13: 3540770542

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This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.


Nonlinear Waves in Integrable and Non-integrable Systems

Nonlinear Waves in Integrable and Non-integrable Systems

Author: Jianke Yang

Publisher: SIAM

Published: 2010-12-02

Total Pages: 452

ISBN-13: 0898717051

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Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical methods for nonintegrable systems is the first of its kind. This book is intended for researchers and graduate students working in applied mathematics and various physical subjects where nonlinear wave phenomena arise (such as nonlinear optics, Bose-Einstein condensates, and fluid dynamics).


Dynamics through First-Order Differential Equations in the Configuration Space

Dynamics through First-Order Differential Equations in the Configuration Space

Author: Jaume Llibre

Publisher: Springer Nature

Published: 2023-05-27

Total Pages: 360

ISBN-13: 3031270959

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The goal of this monograph is to answer the question, is it possible to solve the dynamics problem inside the configuration space instead of the phase space? By introducing a proper class of vector field – the Cartesian vector field – given in a Riemann space, the authors explore the connections between the first order ordinary differential equations (ODEs) associated to the Cartesian vector field in the configuration space of a given mechanical system and its dynamics. The result is a new perspective for studying the dynamics of mechanical systems, which allows the authors to present new cases of integrability for the Suslov and Veselova problem; establish the relation between the Cartesian vector field and the integrability of the geodesic flow in a special class of homogeneous surfaces; discuss the importance of the Nambu bracket in the study of first order ODEs; and offer a solution of the inverse problem in celestial mechanics.