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020 _a9781402061400
_99781402061400
024 7 _a10.1007/1402061404
_2doi
035 _avtls000335494
039 9 _a201509030204
_bVLOAD
_c201404120937
_dVLOAD
_c201404090716
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_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQC5.53
100 1 _aDoktorov, Evgeny V.
_eautor
_9310604
245 1 2 _aA Dressing Method in Mathematical Physics /
_cby Evgeny V. Doktorov, Sergey B. Leble.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2007.
300 _axxiv, 383 p
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aMathematical Physics Studies ;
_v28
500 _aSpringer eBooks
505 0 _aMathematical preliminaries -- Factorization and classical Darboux transformations -- From elementary to twofold elementary Darboux transformation -- Dressing chain equations -- Dressing in 2+1 dimensions -- Applications of dressing to linear problems -- Important links -- Dressing via local Riemann–Hilbert problem -- Dressing via nonlocal Riemann–Hilbert problem -- Generating solutions via ? problem.
520 _aThe monograph is devoted to the systematic presentation of the so called "dressing method" for solving differential equations (both linear and nonlinear) of mathematical physics. The essence of the dressing method consists in a generation of new non-trivial solutions of a given equation from (maybe trivial) solution of the same or related equation. The Moutard and Darboux transformations discovered in XIX century as applied to linear equations, the Bäcklund transformation in differential geometry of surfaces, the factorization method, the Riemann-Hilbert problem in the form proposed by Shabat and Zakharov for soliton equations and its extension in terms of the d-bar formalism comprise the main objects of the book. Throughout the text, a generally sufficient "linear experience" of readers is exploited, with a special attention to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions. Various linear equations of classical and quantum mechanics are solved by the Darboux and factorization methods. An extension of the classical Darboux transformations to nonlinear equations in 1+1 and 2+1 dimensions, as well as its factorization are discussed in detail. The applicability of the local and non-local Riemann-Hilbert problem-based approach and its generalization in terms of the d-bar method are illustrated on various nonlinear equations.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aLeble, Sergey B.
_eautor
_9310605
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9781402061387
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/1-4020-6140-4
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c283236
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