Video library: R. Conte, How to find all elliptic solutions of an ODE: new solution of the cubic-quintic complex Ginzburg--Landau equation

VIDEO LIBRARY


International conference "Geometrical Methods in Mathematical Physics" December 12, 2011 14:45, 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
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