R-matrix approach to integrable systems on time scales

Abstract

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.

21 pages

References in corpus (1)

• Integrable discrete systems on R and related dispersionless systems

Cited by in corpus (4)

• Classical R-matrix theory for bi-Hamiltonian field systems
• A new extended q-deformed KP hierarchy
• The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons
• Bi-Hamiltonian structures for integrable systems on regular time scales