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KP Solitons and the Grassmannians

Part of the SpringerBriefs in Mathematical Physics Book Series (volume 22)

DOI: 10.1007/978-981-10-4094-8

ISBN: 978-981-10-4093-1

Publisher: Springer Singapore - Springer Journals

Mar 25, 2017

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Chapter 1Introduction to KP Theory and KP Solitons

Kodama, Yuji

Pages: 1 –24

[We begin with a study of the Burgers equation, which is the simplest equation combining both nonlinear propagation effects and diffusive effects, and can be used to describe a weak shock phenomena in gas dynamics (see e.g. [131]). The Burgers equation can be linearized by a nonlinear...
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Chapter 2Lax-Sato Formulation of the KP Hierarchy

Kodama, Yuji

Pages: 25 –40

[In this chapter, we briefly review the Lax formulation of the KP hierarchy, which consists of an infinite set of linear equations whose compatibility conditions give rise to the flows corresponding to the KP hierarchy. The main purpose of this section is to highlight the basic framework of...
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Chapter 3Two-Dimensional Solitons

Kodama, Yuji

Pages: 41 –51

[In Chap. 2, we have shown that the KP hierarchy admits particular solutions, called the KP solitons, the main subject of this book, which are expressed by the Wronskian form. In this chapter, we show that this determinant structure is common for other two-dimensional integrable systems generated...
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Chapter 4Introduction to the Real Grassmannian

Kodama, Yuji

Pages: 52 –63

[This chapter gives a brief introduction to the real Grassmannian \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 5The Deodhar Decomposition for the Grassmannian and the Positivity

Kodama, Yuji

Pages: 64 –89

[In this chapter, we start to review the flag variety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 6Classification of KP Solitons

Kodama, Yuji

Pages: 90 –102

[This chapter concerns with a classification problem of the asymptotic spatial structure of “regular” KP solitons for large |y| using the Deodhar decomposition of the Grassmannian. More precisely, we consider the soliton solution from a point A represented by an \documentclass[12pt]{minimal}...
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Chapter 7KP Solitons on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Gr}(N, 2N)_{\ge 0}$$\end{document}

Kodama, Yuji

Pages: 103 –119

[In this chapter, we will discuss the reflective symmetry \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
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Chapter 8Soliton Graphs

Kodama, Yuji

Pages: 120 –132

[In this chapter, we explicitly construct the soliton graph \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...

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