Using the Fourier-Laplace transform, we describe the isomonodromy equations for meromorphic connections on the Riemann sphere with unramified irregular singularities as those for connections with a (possibly ramified) irregular singularity and a regular singularity. This generalizes some results of Harnad and Woodhouse.
We consider the initial-boundary value problem for a 2-speed system of first order semilinear hyperbolic equations. We establish the existence of global weak solutions in L1 by the theory of nonlinear contraction semigroups. Using the monotone method and the div-curl lemma, we investigate the hydrodynamical limits of the solutions of the hyperbolic systems and show that the limits verify the doubly nonlinear parabolic equations.
We study the classical problem of the computation of a complete system of Stokes matrices in terms of connection coefficients. Stokes matrices refer to a linear system of ODEs with Poincaré rank one and semi-simple leading matrix, while the connection coefficients connect solutions of the associated hypergeometric system of ODEs. The problem here is solved with no assumptions on the residue matrix at zero of the system of Poincaré rank one, so extending method and results of .