Kp Solitons And The Grassmannians
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Kp Solitons And The Grassmannians
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Author : Yuji Kodama
language : en
Publisher: Springer
Release Date : 2017-03-24
Kp Solitons And The Grassmannians written by Yuji Kodama and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-24 with Science categories.
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.
Glimpses Of Soliton Theory
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Author : Alex Kasman
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Glimpses Of Soliton Theory written by Alex Kasman 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 2010 with Mathematics categories.
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. --
Solitons In Two Dimensional Shallow Water
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Author : Yuji Kodama
language : en
Publisher: SIAM
Release Date : 2018-12-10
Solitons In Two Dimensional Shallow Water written by Yuji Kodama and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-10 with Science categories.
Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools?algebraic geometry, algebraic combinatorics, and representation theory, among others?are used to analyze these two-dimensional wave patterns. The author?s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.
Tau Functions And Their Applications
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Author : John Harnad
language : en
Publisher: Cambridge University Press
Release Date : 2021-02-04
Tau Functions And Their Applications written by John Harnad 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 2021-02-04 with Mathematics categories.
A thorough introduction to tau functions, from the basics through to the most recent results, with applications in mathematical physics.
Algebras Quivers And Representations
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Author : Aslak Bakke Buan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-24
Algebras Quivers And Representations written by Aslak Bakke Buan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-24 with Mathematics categories.
This book features survey and research papers from The Abel Symposium 2011: Algebras, quivers and representations, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like, commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulate categories.
Grassmannian Geometry Of Scattering Amplitudes
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Author : Nima Arkani-Hamed
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-05
Grassmannian Geometry Of Scattering Amplitudes written by Nima Arkani-Hamed 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 2016-05-05 with Mathematics categories.
An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.
Nonlinear Dispersive Equations
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Author : Christian Klein
language : en
Publisher: Springer Nature
Release Date : 2021
Nonlinear Dispersive Equations written by Christian Klein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Differential equations categories.
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Nonlinear Waves And Solitons On Contours And Closed Surfaces
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Author : Andrei Ludu
language : en
Publisher: Springer Nature
Release Date : 2022-11-04
Nonlinear Waves And Solitons On Contours And Closed Surfaces written by Andrei Ludu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-04 with Science categories.
This new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics. The book has a Foreword by Jerry L. Bona and Hongqiu Chen. The book is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering.
Functional Analysis And Geometry Selim Grigorievich Krein Centennial
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Author : Peter Kuchment
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-07-26
Functional Analysis And Geometry Selim Grigorievich Krein Centennial written by Peter Kuchment 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 2019-07-26 with Festschriften categories.
This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.
Perspectives In Lie Theory
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Author : Filippo Callegaro
language : en
Publisher: Springer
Release Date : 2017-12-07
Perspectives In Lie Theory written by Filippo Callegaro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-07 with Mathematics categories.
Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.