Browsing by Subject "dispersionless systems"

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    Integrable systems on regular time scales
    (2009) Yantır, Burcu Silindir
    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.