{"product_id":"painleve-equations-in-the-differential-geometry-of-surfaces-von-ulrich-eitner-alexander-i-bobenko-tu-berlin","title":"Painleve Equations in the Differential Geometry of Surfaces","description":"\u003cp\u003eSince the time of surfaces -+ in differential Gauss, parametrized (x, y) P(x, y) have been described a frame attached to the moving geometry through TI(x, y) surface. One introduces the Gauss- which linear dif- Weingarten equations are , ferential equations = U = TIX T1, VT', !PY (1. for the and their condition frame, compatibility - = V + [U, V] 0, UY (1.2) which the Gauss-Codazzi For surfaces in three-dim- represents equations . a sional Euclidean the frame T1 lies in the usually or space, group SO(3) SU(2). On the other a of a non-linear in the form hand, representation equation (1.2) is the of the of of starting point theory integrable equations (theory solitons), which in mathematical in the 1960's appeared physics [NMPZ, AbS, CD, FT, More the differential for the coefficients of AbC]. exactly, partial equation (1.2) the matrices U and V is considered to be if these matrices can be integrable , extended to U V non-trivially a one-parameter family (x, y, A), (x, y, A) satisfying - = + U(A)y V(A). [U(A), V(A)] 0, (1-3) so that the differential is and original partial equation preserved.' . Usually U(A) V are rational functions of the which is called the (A) parameter A, spectral param- In soliton the eter is called the Lax . theory, representation (1.3) representation the Zakharov-Shabat or representation [ZS].\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783540414148\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783540414148","offer_id":39437859225693,"sku":"9783540414148","price":37.4,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/b2a6be7c-09c1-424a-b737-f1a474900e4d.jpg?v=1772086651","url":"https:\/\/shop.autorenwelt.de\/products\/painleve-equations-in-the-differential-geometry-of-surfaces-von-ulrich-eitner-alexander-i-bobenko-tu-berlin","provider":"Autorenwelt Shop","version":"1.0","type":"link"}