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Integrable couplings, bi‐integrable couplings and their Hamiltonian structures of the Giachetti–Johnson soliton hierarchy
Author(s) -
Tang YaNing,
Wang Lei,
Ma WenXiu
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3222
Subject(s) - integrable system , mathematics , hamiltonian (control theory) , loop algebra , soliton , hierarchy , curvature , mathematical physics , pure mathematics , algebra over a field , quantum mechanics , nonlinear system , physics , geometry , current algebra , mathematical optimization , economics , market economy
On the basis of zero curvature equations from semi‐direct sums of Lie algebras, we construct integrable couplings of the Giachetti–Johnson hierarchy of soliton equations. We also establish Hamiltonian structures of the resulting integrable couplings by the variational identity. Moreover, we obtain bi‐integrable couplings of the Giachetti–Johnson hierarchy and their Hamiltonian structures by applying a class of non‐semisimple matrix loop algebras consisting of triangular block matrices. Copyright © 2014 John Wiley & Sons, Ltd.