000			03511nam a22005055i 4500
001			978-1-4020-6140-0
003			DE-He213
005			20251006084529.0
007			cr nn 008mamaa
008			100301s2007 ne | s |||| 0|eng d
020			_a9781402061400
020			_a99781402061400
024	7		_a10.1007/1-4020-6140-4 _2doi
082	0	4	_a530.15 _223
100	1		_aDoktorov, Evgeny V. _eauthor.
245	1	2	_aA Dressing Method in Mathematical Physics _h[electronic resource] / _cby Evgeny V. Doktorov, Sergey B. Leble.
264		1	_aDordrecht : _bSpringer Netherlands, _c2007.
300			_aXXIV, 383 p _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aMathematical Physics Studies ; _v28
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.
650		0	_aPHYSICS.
650		0	_aALGEBRA.
650		0	_aFUNCTIONS OF COMPLEX VARIABLES.
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aELECTRODYNAMICS.
650	1	4	_aPHYSICS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aNON-ASSOCIATIVE RINGS AND ALGEBRAS.
650	2	4	_aFUNCTIONS OF A COMPLEX VARIABLE.
650	2	4	_aCLASSICAL ELECTRODYNAMICS, WAVE PHENOMENA.
700	1		_aLeble, Sergey B. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781402061387
830		0	_aMathematical Physics Studies ; _v28
856	4	0	_uhttp://dx.doi.org/10.1007/1-4020-6140-4 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-PHA
942			_2ddc _cER
999			_c61588 _d61588