LEADER 03825nam 2200697Ia 450 001 9910453268303321 005 20200520144314.0 010 $a1-281-91343-X 010 $a9786611913434 010 $a1-4020-8491-9 024 7 $a10.1007/978-1-4020-8491-1 035 $a(CKB)1000000000546860 035 $a(EBL)418083 035 $a(OCoLC)311507109 035 $a(SSID)ssj0000217518 035 $a(PQKBManifestationID)11228295 035 $a(PQKBTitleCode)TC0000217518 035 $a(PQKBWorkID)10211590 035 $a(PQKB)10801318 035 $a(DE-He213)978-1-4020-8491-1 035 $a(MiAaPQ)EBC418083 035 $a(MiAaPQ)EBC5292441 035 $a(PPN)132860570 035 $a(Au-PeEL)EBL418083 035 $a(CaPaEBR)ebr10266902 035 $a(CaONFJC)MIL1101486 035 $a(Au-PeEL)EBL5292441 035 $a(CaONFJC)MIL191343 035 $a(EXLCZ)991000000000546860 100 $a20080402d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Painleve? handbook$b[electronic resource] /$fRobert Conte, Micheline Musette 205 $a1st ed. 2008. 210 $aDordrecht $cSpringer$dc2008 215 $a1 online resource (273 p.) 300 $aDescription based upon print version of record. 311 $a94-007-9627-7 311 $a1-4020-8490-0 320 $aIncludes bibliographical references (p. 234-252) and index. 327 $aIntroduction; Singularity Analysis: Painleve? Test; Integrating Ordinary Differential Equations; Partial Differential Equations: Paieleve? Test; From the Test to Explicit Solutions of PDEs; Integration of Hamiltonian Systems; Discrete Nonlinear Equations; FAQ (Frequently Asked Questions) 330 $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 Painlevé test. If the equation under study passes the Painlevé 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 Schrödinger equation (continuous and discrete), the Korteweg-de Vries equation, the Hénon-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. 606 $aPainleve? equations 606 $aMathematical physics 608 $aElectronic books. 615 0$aPainleve? equations. 615 0$aMathematical physics. 676 $a515.352 676 $a518/.6 700 $aConte$b Robert$f1943-$0891610 701 $aMusette$b Micheline$0731201 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453268303321 996 $aThe Painleve? handbook$92441660 997 $aUNINA