000			03327nam a22005415i 4500
001			978-1-4020-8491-1
003			DE-He213
005			20160302163418.0
007			cr nn 008mamaa
008			100301s2008 ne | s |||| 0|eng d
020			_a9781402084911 _9978-1-4020-8491-1
024	7		_a10.1007/978-1-4020-8491-1 _2doi
050		4	_aQC5.53
072		7	_aPHU _2bicssc
072		7	_aSCI040000 _2bisacsh
082	0	4	_a530.15 _223
100	1		_aConte, Robert. _eauthor.
245	1	4	_aThe Painlev� Handbook _h[electronic resource] / _cby Robert Conte, Micheline Musette.
264		1	_aDordrecht : _bSpringer Netherlands, _c2008.
300			_aXXIII, 256 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
520			_aNonlinear differential or difference equations are encountered not only in mathematics, but also in many areas of physics (evolution equations, propagation of a signal in an optical fiber), chemistry (reaction-diffusion systems), and biology (competition of species). This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlev� test. If the equation under study passes the Painlev� test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions. The examples chosen to illustrate these methods are mostly taken from physics. These include on the integrable side the nonlinear Schr�dinger equation (continuous and discrete), the Korteweg-de Vries equation, the H�non-Heiles Hamiltonians, on the nonintegrable side the complex Ginzburg-Landau equation (encountered in optical fibers, turbulence, etc), the Kuramoto-Sivashinsky equation (phase turbulence), the Kolmogorov-Petrovski-Piskunov equation (KPP, a reaction-diffusion model), the Lorenz model of atmospheric circulation and the Bianchi IX cosmological model. Written at a graduate level, the book contains tutorial text as well as detailed examples and the state of the art on some current research.
650		0	_aPhysics.
650		0	_aChemometrics.
650		0	_aDynamics.
650		0	_aErgodic theory.
650		0	_aDifferential equations.
650		0	_aPartial differential equations.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650	1	4	_aPhysics.
650	2	4	_aMathematical Methods in Physics.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aOrdinary Differential Equations.
650	2	4	_aPartial Differential Equations.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
650	2	4	_aMath. Applications in Chemistry.
700	1		_aMusette, Micheline. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781402084904
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4020-8491-1
912			_aZDB-2-PHA
999			_c180934 _d180934