The Painlevé Handbook
Nonlinear 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...
Gorde:
| Egile Nagusiak: | , |
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| Formatua: | Livre numérique |
| Hizkuntza: | Anglais |
| Argitaratua: |
Dordrecht :
Springer Netherlands : Springer e-books
[20..].
Cham : Springer Nature |
| Gaiak: | |
| Sarrera elektronikoa: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Oharra: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Painlevé handbook, Robert Conte, Micheline Musette, 2008, [Dordrecht], Springer, 1 vol. (XXIII-256 p.), 978-1-402-08490-4 |
| Gaia: | Nonlinear 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 |
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| Alearen deskribapena: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9781402084911 |
| Sartu: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |