R-matrix approach to integrable systems on time scales

Details R-matrix approach to integrable systems on time scales R-matrix approach to integrable systems on time scales

2008-03-10

arxiv.org/abs/0803.1439v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages

Scientific paper

10.1088/1751-8113/41/38/385203

A general unifying framework for integrable soliton-like systems on time scales is introduced. The $R$-matrix formalism is applied to the algebra of $\delta$-differential operators in terms of which one can construct infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are difference counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.

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