Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2009.Thesis (Ph.D.) -- Bilkent University, 2009.Includes bibliographical references leaves 98-102.We present two approaches to unify the integrable systems. Both approaches are
based on the classical R-matrix formalism. The first approach proceeds from the
construction of (1 + 1)-dimensional integrable ∆-differential systems on regular
time scales together with bi-Hamiltonian structures and conserved quantities.
The second approach is established upon the general framework of integrable
discrete systems on R and integrable dispersionless systems. We discuss the
deformation quantization scheme for the dispersionless systems. We also apply
the theories presented in this dissertation, to several well-known examples.Yantır, Burcu SilindirPh.D
