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arXiv · 0707.1084

Integrable discrete systems on R and related dispersionless systems

Maciej Blaszak·Metin Gurses·Burcu Silindir·Blazej M. Szablikowski
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Abstract

The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter groups of diffeomorphisms, through which one can define algebras of shift operators is introduced. Two integrable hierarchies of discrete chains together with bi-Hamiltonian structures are constructed. Their continuous limit and the inverse problem based on the deformation quantization scheme are considered.

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Maciej Blaszak, Metin Gurses, Burcu Silindir, Blazej M. Szablikowski. 2007-07-07. Integrable discrete systems on R and related dispersionless systems. https://doi.org/10.1063/1.2948962

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