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Construction scheme for discrete Miura transformations. (English) Zbl 0844.65090
Summary: A direct and elementary scheme for the construction of Miura-type transformations and discrete differential equations related to them (scalar and vector) is presented. The scheme is illustrated using as examples the Volterra and Toda models. A discrete differential analogue of the Calogero-Degasperis equation is discussed in detail. This example is used to show how to construct conservation laws, higher symmetries, and solutions for an equation obtained with the help of the scheme.

MSC:
65Z05Applications of numerical analysis to physics
35Q58Other completely integrable PDE (MSC2000)
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
35Q53KdV-like (Korteweg-de Vries) equations