LAX CONSTRAINTS IN SEMISIMPLE LIE GROUPS

Instead of studying Lax equations as such, a solution Z of aLax equation is assumed to be given. Then Z is regarded as defininga constraint on a non-autonomous linear differential equationassociated with the Lax equation. In generic cases, quadratureand sometimes algebraic formulae in terms of Z are then provedfor solution x of the linear differential equation, and examplesare given where these formulae lead to new results in higher-ordervariational problems for curves in general semisimple Lie groupsG, extending results previously obtained by different methodsfor the case where G has dimension 3. The new construction isexplored in detail for G = SU(m).