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The direct method in soliton theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	530.12/4
書名/作者:	The direct method in soliton theory // Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson.
作者:	Hirota, Ryōgo,
其他作者:	Nagai, Atsushi,
面頁冊數:	1 online resource (xi, 200 pages) : : digital, PDF file(s).
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Solitons.
ISBN:	9780511543043 (ebook)
內容註:	1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index.
摘要、提要註:	The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.
電子資源:	http://dx.doi.org/10.1017/CBO9780511543043

The direct method in soliton theory /
Hirota, Ryōgo,1932-

The direct method in soliton theory /Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson. - 1 online resource (xi, 200 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;155. - Cambridge tracts in mathematics ;169..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index.

The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.

ISBN: 9780511543043 (ebook)Subjects--Topical Terms:

383586
Solitons.

LC Class. No.: QC174.26.W28 / H4713 2004

Dewey Class. No.: 530.12/4

The direct method in soliton theory /
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505 0 $a 1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index.
520 $a The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.
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