Document Type
Journal Article
Department/Unit
Department of Computer Science
Title
Two enlarged loop algebras for obtaining new integrable hierarchies
Language
English
Abstract
Taking a loop algebra B̄2 we obtain an integrable soliton hierarchy which is similar to the well-known KaupNewell (KN) hierarchy, but it is not. We call it a modified KN (mKN) hierarchy. Then two new enlarged loop algebras of the loop algebra B̄2 are established, respectively, which are used to establish isospectral problems. Thus, two various types of integrable soliton-equation hierarchies along with multi-component potential functions are obtained. Their Hamiltonian structures are also obtained by the variational identity. The second hierarchy is integrable couplings of the mKN hierarchy. This paper provides a clue for generating loop algebras, specially, gives an approach for producing new integrable systems. If we obtain a new soliton hierarchy, we could deduce its symmetries, conserved laws, Darboux transformations, soliton solutions and so on. Hence, the way presented in the paper is an important aspect to obtain new integrable systems in soliton theory. © 2011 World Scientific Publishing Company.
Keywords
Hamiltonian structure, integrable system, Loop algebra
Publication Date
2011
Source Publication Title
International Journal of Modern Physics B
Volume
25
Issue
19
Start Page
2637
End Page
2656
Publisher
World Scientific Publishing
DOI
10.1142/S0217979211100904
Link to Publisher's Edition
http://dx.doi.org/10.1142/S0217979211100904
ISSN (print)
02179792
ISSN (electronic)
17936578
APA Citation
Zhang, Y., Tam, H., & Jiang, W. (2011). Two enlarged loop algebras for obtaining new integrable hierarchies. International Journal of Modern Physics B, 25 (19), 2637-2656. https://doi.org/10.1142/S0217979211100904