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We show that all local holomorphic solutions of matrix soliton equations of parabolic type admit an analytic continuation to globally meromorphic functions of a spatial variable. As examples, we consider the matrix Korteweg–de Vries equation and the matrix modified Korteweg–de Vries equation, as well as various versions of the matrix nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering transform. Some higher analogs of Painlevé equations are considered as examples. [ABSTRACT FROM AUTHOR]