Düzgün zaman skalasında integre edilebilir sistemler

We present two approaches to unify the integrable systems. Bothapproaches are based on the classical R-matrix formalism. Thefirst approach proceeds from the construction of(1+1)-dimensional integrable \Delta-differential systems onregular time scales together with bi-Hamiltonian structures andconserved quantities. The second approach is established upon thegeneral framework of integrable discrete systems on Real numbers andintegrable dispersionless systems. We discuss the deformationquantization scheme for the dispersionless systems. We also applythe theories presented in this dissertation, to several well-knownexamples.