LEADER 04182nam 22006255 450 001 9910254280903321 005 20200704103452.0 010 $a981-10-4094-X 024 7 $a10.1007/978-981-10-4094-8 035 $a(CKB)3710000001127305 035 $a(DE-He213)978-981-10-4094-8 035 $a(MiAaPQ)EBC4829894 035 $a(PPN)199765197 035 $a(EXLCZ)993710000001127305 100 $a20170324d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKP Solitons and the Grassmannians $eCombinatorics and Geometry of Two-Dimensional Wave Patterns /$fby Yuji Kodama 205 $a1st ed. 2017. 210 1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2017. 215 $a1 online resource (XII, 138 p. 19 illus.) 225 1 $aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v22 311 $a981-10-4093-1 320 $aIncludes bibliographical references. 327 $a1 Introduction to KP theory and KP solitons -- 2 Lax-Sato formulation of the KP hierarchy -- 3 Two-dimensional 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. 330 $aThis is the first book to treat combinatorial and geometric aspects of two-dimensional solitons. Based on recent research by the author and his collaborators, the book presents new developments focused on an interplay between the theory of solitons and the combinatorics of finite-dimensional Grassmannians, in particular, the totally nonnegative (TNN) parts of the Grassmannians. The book begins with a brief introduction to the theory of the Kadomtsev?Petviashvili (KP) equation and its soliton solutions, called the KP solitons. Owing to the nonlinearity in the KP equation, the KP solitons form very complex but interesting web-like patterns in two dimensions. These patterns are referred to as soliton graphs. The main aim of the book is to investigate the detailed structure of the soliton graphs and to classify these graphs. It turns out that the problem has an intimate connection with the study of the TNN part of the Grassmannians. The book also provides an elementary introduction to the recent development of the combinatorial aspect of the TNN Grassmannians and their parameterizations, which will be useful for solving the classification problem. This work appeals to readers interested in real algebraic geometry, combinatorics, and soliton theory of integrable systems. It can serve as a valuable reference for an expert, a textbook for a special topics graduate course, or a source for independent study projects for advanced upper-level undergraduates specializing in physics and mathematics. 410 0$aSpringerBriefs in Mathematical Physics,$x2197-1757 ;$v22 606 $aMathematical physics 606 $aDifference equations 606 $aFunctional equations 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 615 0$aMathematical physics. 615 0$aDifference equations. 615 0$aFunctional equations. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 14$aMathematical Physics. 615 24$aDifference and Functional Equations. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a530.124 700 $aKodama$b Yuji$4aut$4http://id.loc.gov/vocabulary/relators/aut$0733250 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254280903321 996 $aKP Solitons and the Grassmannians$91561702 997 $aUNINA