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Title: Two-component coupled KdV equations and its connection with the generalized Harry Dym equations

It is shown that three different Lax operators in the Dym hierarchy produce three generalized coupled Harry Dym equations. These equations transform, via the reciprocal link, to the coupled two-component Korteweg de Vries (KdV) system. The first equation gives us known integrable two-component KdV system, while the second reduces to the known symmetrical two-component KdV equation. The last one reduces to the Drienfeld-Sokolov equation. This approach gives us new Lax representation for these equations.
Authors:
 [1]
  1. Institute of Theoretical Physics, University of Wrocław, Wrocław pl. M. Borna 9, 50-205 Wrocław (Poland)
Publication Date:
OSTI Identifier:
22251661
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONSERVATION LAWS; KORTEWEG-DE VRIES EQUATION; LAX THEOREM; MATHEMATICAL OPERATORS