Bers and Hénon, Painlevé and Schrödinger
نویسندگان
چکیده
منابع مشابه
2 00 6 Painlevé Property of the Hénon - Heiles Hamiltonians
— Time independent Hamiltonians of the physical type H = (P 2 1 + P 2 2 )/2 + V (Q1, Q2) pass the Painlevé test for only seven potentials V , known as the Hénon-Heiles Hamiltonians, each depending on a finite number of free constants. Proving the Painlevé property was not yet achieved for generic values of the free constants. We integrate each missing case by building a birational transformatio...
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A useful semiclassical method to calculate eigenfunctions of the Schrödinger equation is the mapping to a well-known ordinary differential equation, as for example Airy’s equation. In this paper we generalize the mapping procedure to the nonlinear Schrödinger equation or Gross-Pitaevskii equation describing the macroscopic wave function of a Bose-Einstein condensate. The nonlinear Schrödinger e...
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— The paper consists of two parts. In the first part, we explain an excellent idea, due to mathematicians of the 19-th century, of naturally developing classical Galois theory of algebraic equations to an infinite dimensional Galois theory of nonlinear differential equations. We show with an instructive example how we can realize the idea of the 19-th century in a rigorous framework. In the sec...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2009
ISSN: 0012-7094
DOI: 10.1215/00127094-2009-042