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Explicit integration of classical series of exponential systems using the approach of Darboux-Moutard-Goursat

Wednesday 31st October 2001 - 11:00 to 12:00
INI Seminar Room 1
We give the basic facts about the current state and different generalisations of the problem first studied by Gaspar Monge: given one (!) ODE for two (!) functions
F(x, y, y', z, z') = 0, y = y(x), z = z(x), (1)

is it possible to give its complete parametric solution
x = x(t, u, u', u'', ...),
y = y(t, u, u', u'', ...),
z = z(t, u, u', u'', ...),

where t is a new parameter, and u = u(t) is a new arbitrary function ?
Recently problems of similar form found applications in optimal control ("flat systems of ODEs"). Obviously this problem also deserves attention in the framework of integrable systems.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons