2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165699This paper is devoted to studying the initial value problem for a third-order dispersive equation for closed curves into Kähler manifolds. This equation is a geometric generalization of a two-sphere valued system modeling the motion of vortex filament. We prove the local existence theorem by using geometric analysis and classical energy method.25pages, final versionAnalysis of PDEs53C44; 35Q53text