6533b837fe1ef96bd12a2455
RESEARCH PRODUCT
L'identité de Fay en théorie des systèmes intégrables
Caroline Kallasubject
Identité de FayOvale réelSolutions algébro-géométriques[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Equation de Camassa-HolmBase d'homologieAlgorithme de Tretkoff-TretkoffEquation de Schrödinger non linéaire vectorielle[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Equation de Davez-StewartsonEDPApplication d'uniformisationCourbe algébriqueSurface de Riemann[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Breather rationnelSolitonDégénérescence de surface de RiemannFonction thêtaNo english keywordsPériodes de différentielles holomorphesThêta diviseurdescription
Fay's identity on Riemann surfaces is a powerful tool in the context of algebro-geometric solutions to integrable equations. This relation generalizes a well-known identity for the cross-ratio function in the complex plane. It allows to establish relations between theta functions and their derivatives. This offers a complementary approach to algebro-geometric solutions of integrable equations with certain advantages with respect to the use of Baker-Akhiezer functions. It has been successfully applied by Mumford et al. to the Korteweg-de Vries, Kadomtsev-Petviashvili and sine-Gordon equations. Following this approach, we construct algebro-geometric solutions to the Camassa-Holm and Dym type equations, as well as solutions to the multi-component nonlinear Schrödinger equation and the Davey-Stewartson equations. Solitonic limits of these solutions are investigated when the genus of the associated Riemann surface drops to zero. Moreover, we present a numerical evaluation of algebro-geometric solutions of integrable equations when the associated Riemann surface is real.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-06-27 |