2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196220We present a noncommutative generalization of Lax formalism of U(N) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative Bäcklund transformation and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model.1+20 pagesHigh Energy Physics - Theorytext