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Combinatorial Aspect of Integrable Systems

2007 Mathematics
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Release : 2007
Genre : Mathematics
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Book Synopsis Combinatorial Aspect of Integrable Systems by : Arkady Berenstein

Download or read book Combinatorial Aspect of Integrable Systems written by Arkady Berenstein. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of six papers based on the expository lectures of the workshop "Combinatorial Aspect of Integrable Systems" held at RIMS during July 26-30, 2004, as a part of the Project Research 2004 "Method of Algebraic Analysis in Integrable Systems". The topics range over crystal bases of quantum groups, its algebra-geometric analogue known as geometric crystal, generalizations of Robinson-Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang-Baxter maps, and integrable discrete dynamics. All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Combinatorial aspect of integrable systems

2005
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Release : 2005
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Book Synopsis Combinatorial aspect of integrable systems by : Atsuo Kuniba

Download or read book Combinatorial aspect of integrable systems written by Atsuo Kuniba. This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt:

KP Solitons and the Grassmannians

2017-03-24 Science
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Release : 2017-03-24
Genre : Science
Kind : eBook
Book Rating : 94X/5 ( reviews)

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Book Synopsis KP Solitons and the Grassmannians by : Yuji Kodama

Download or read book KP Solitons and the Grassmannians written by Yuji Kodama. This book was released on 2017-03-24. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev–Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of the combinatorial aspect of the TNN Grassmannians and their parameterizations, which will be useful for solving the classification problem. This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. It can serve as a valuable reference for an expert, a textbook for a special topics graduate course, or a source for independent study projects for advanced upper-level undergraduates specializing in physics and mathematics.

Symmetries, Integrable Systems and Representations

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 630/5 ( reviews)

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Book Synopsis Symmetries, Integrable Systems and Representations by : Kenji Iohara

Download or read book Symmetries, Integrable Systems and Representations written by Kenji Iohara. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

New Trends In Quantum Integrable Systems - Proceedings Of The Infinite Analysis 09

2010-10-29 Mathematics
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Release : 2010-10-29
Genre : Mathematics
Kind : eBook
Book Rating : 926/5 ( reviews)

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Book Synopsis New Trends In Quantum Integrable Systems - Proceedings Of The Infinite Analysis 09 by : Boris Feigin

Download or read book New Trends In Quantum Integrable Systems - Proceedings Of The Infinite Analysis 09 written by Boris Feigin. This book was released on 2010-10-29. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project “Method of Algebraic Analysis in Integrable Systems” in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics.Through these topics, the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

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