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International conference "Geometrical Methods in Mathematical Physics"
December 12, 2011 14:45–15:30, Moscow, Lomonosov Moscow State University
 


How to find all elliptic solutions of an ODE: new solution of the cubic-quintic complex Ginzburg–Landau equation

R. Conte

École normale supérieure de Cachan
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R. Conte


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Abstract: Given a nonlinear $N$-th order algebraic ordinary differential equation (ODE) which fails the Painlevé test, a major problem in physics is to find explicitly its general analytic solution, i.e. the largest $M$ -parameter particular solution without movable critical singularities, with $ M$ strictly lower than $N$. We present here two results and one application.
The first result follows from Clunie's lemma of Nevanlinna theory: under two assumptions which happen to be true for most physically relevant nonintegrable ODE's, any meromorphic solution is necessarily elliptic.

Language: English

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