Integrable discrete systems on R and related dispersionless systems
Journal of Mathematical Physics
American Institute of Physics
072702-1 - 072702-17
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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.