2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171046In this paper, we consider the Klein-Gordon-Schrödinger system with the higher order Yukawa coupling in $ \mathbb{R}^{1+1} $, and prove the local and global wellposedness in $L^2\times H^{1/2}$. The method to be used is adapted from the scheme originally by Colliander J., Holmer J., Tzirakis N. \cite{CoHT06} to use the available $L^2$ conservation law of $u$ and control the growth of $n$ via the estimates in the local theory.13 pages, 3 figuresAnalysis of PDEs35L15, 35Q55text