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101 0 $aeng
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181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 14$aThe direct method in soliton theory /$fRyogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson$b[electronic resource]
210  1$aCambridge :$cCambridge University Press,$d2004.
215   $a1 online resource (xi, 200 pages) $cdigital, PDF file(s)
225 1 $aCambridge tracts in mathematics ;$v155
300   $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
311   $a0-521-83660-3 
320   $aIncludes bibliographical references (p. 195-197) and index.
327   $a1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index.
330   $aThe bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as  a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.
410  0$aCambridge tracts in mathematics ;$v155.
606   $aSolitons
615  0$aSolitons.
676   $a530.12/4
700   $aHirota$b Ryo?go$f1932-$0291230
702   $aNagai$b Atsushi
702   $aNimmo$b J. J. C$g(Jonathan J. C.),
702   $aGilson$b Claire
801  0$bUkCbUP
801  1$bUkCbUP
906   $aBOOK
912   $a9910457717203321
996   $aDirect method in soliton theory$9748606
997   $aUNINA