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Zbl 0844.65090
Yamilov, Ravil I.
Construction scheme for discrete Miura transformations. (English)
[J] J. Phys. A, Math. Gen. 27, No.20, 6839-6851 (1994). ISSN 0305-4470

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 2000:: *65Z05 Applications to physics
35Q58 Other completely integrable PDE
37J35 Completely integrable systems, etc.
37K10 Completely integrable systems etc.
35Q53 KdV-like equations

Keywords: Korteweg-de Vries equation; Miura-type transformations; discrete differential equations; Volterra and Toda models; Calogero-Degasperis equation; conservation laws; symmetries

Cited in: Zbl 0873.34067

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