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    Integrable discrete systems on R and related dispersionless systems
    (American Institute of Physics, 2008) Blaszak, M.; Gurses, M.; Silindir, B.; Szablikowski, B. M.
    A general framework for integrable discrete systems on ℝ, in particular, containing lattice soliton systems and their q-deformed analogs, is presented. The concept of regular grain structures on R, generated by discrete one-parameter groups of diffeomorphisms, in terms of which one can define algebra of shift operators is introduced. Two integrable hierarchies of discrete chains together with bi-Hamiltonian structures and their continuous limits are constructed. The inverse problem based on the deformation quantization scheme is considered. © 2008 American Institute of Physics.