The Resource KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource)
KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource)
Resource Information
The item KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This is the first book to treat combinatorial and geometric aspects of twodimensional 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 finitedimensional 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 weblike 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 upperlevel undergraduates specializing in physics and mathematics.
 Language
 eng
 Extent
 1 online resource (XII, 138 pages)
 Contents

 1 Introduction to KP theory and KP solitons
 2 LaxSato formulation of the KP hierarchy
 3 Twodimensional solitons
 4 Introduction to the real Grassmannian
 5 The Deodhar decomposition for the Grassmannian and the positivity
 6 Classification of KP solitons
 7 KP Solitons on Gr(N,2N)≥0
 8 Soliton graphs
 References
 Isbn
 9789811040948
 Label
 KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns
 Title
 KP Solitons and the Grassmannians
 Title remainder
 Combinatorics and Geometry of TwoDimensional Wave Patterns
 Statement of responsibility
 by Yuji Kodama
 Language
 eng
 Summary
 This is the first book to treat combinatorial and geometric aspects of twodimensional 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 finitedimensional 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 weblike 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 upperlevel undergraduates specializing in physics and mathematics.
 Assigning source
 Provided by publisher
 http://library.link/vocab/creatorName
 Kodama, Yuji
 Image bit depth
 0
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement

 Springer eBooks
 SpringerBriefs in Mathematical Physics,
 Series volume
 22
 http://library.link/vocab/subjectName

 Mathematics
 Difference equations
 Functional equations
 Global analysis (Mathematics)
 Manifolds (Mathematics)
 Mathematical physics
 Label
 KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1 Introduction to KP theory and KP solitons  2 LaxSato formulation of the KP hierarchy  3 Twodimensional solitons  4 Introduction to the real Grassmannian  5 The Deodhar decomposition for the Grassmannian and the positivity  6 Classification of KP solitons  7 KP Solitons on Gr(N,2N)≥0  8 Soliton graphs  References
 Control code
 9789811040948
 Dimensions
 unknown
 Extent
 1 online resource (XII, 138 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9789811040948
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9789811040948
 Other physical details
 19 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)980303630
 Label
 KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1 Introduction to KP theory and KP solitons  2 LaxSato formulation of the KP hierarchy  3 Twodimensional solitons  4 Introduction to the real Grassmannian  5 The Deodhar decomposition for the Grassmannian and the positivity  6 Classification of KP solitons  7 KP Solitons on Gr(N,2N)≥0  8 Soliton graphs  References
 Control code
 9789811040948
 Dimensions
 unknown
 Extent
 1 online resource (XII, 138 pages)
 File format
 multiple file formats
 Form of item

 online
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9789811040948
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9789811040948
 Other physical details
 19 illustrations
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)980303630
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/KPSolitonsandtheGrassmanniansCombinatorics/Al7ldRgwDM8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/KPSolitonsandtheGrassmanniansCombinatorics/Al7ldRgwDM8/">KP Solitons and the Grassmannians : Combinatorics and Geometry of TwoDimensional Wave Patterns, by Yuji Kodama, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>