The R-matrix approach to integrable systems on time scales

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Blaszak M., Silindir B., Szablikowski B. M.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol.41, no.38, 2008 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 41 Issue: 38
• Publication Date: 2008
• Doi Number: 10.1088/1751-8113/41/38/385203
• Journal Name: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Dokuz Eylül University Affiliated: No

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 an infinite hierarchy of commuting vector fields. The theory is illustrated by two infinite-field integrable hierarchies on time scales which are Delta-differential counterparts of KP and mKP. The difference counterparts of AKNS and Kaup-Broer soliton systems are constructed as related finite-field restrictions.