2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145873In \cite{kri02}, I. M. Krichever invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation \cite{hit87}. We study a necessary and sufficient condition for the linearity of flows on the space of Krichever-Lax matrices in a Lax representation in terms of cohomological classes using the similar technique and analysis from the work \cite{grif85} by P. A. Griffiths.Dynamical SystemsAlgebraic Geometry14F05; 14H70; 32L10; 58F07text