Applications of a Few Lie Algebras

Two isomorphic groups R2 and M are firstly constructed. Then we extend them into the differential manifold R2n and n products of the group M for which four kinds of Lie algebras are obtained. By using these Lie algebras and the Tu scheme, integrable hierarchies of evolution equations along with mult...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2016-06, Vol.32 (2), p.289-304
Main Authors: Zhang, Yu-feng, Han, Zhong, Zhao, Zhong-long
Format: Article
Language:English
Subjects:
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:Two isomorphic groups R2 and M are firstly constructed. Then we extend them into the differential manifold R2n and n products of the group M for which four kinds of Lie algebras are obtained. By using these Lie algebras and the Tu scheme, integrable hierarchies of evolution equations along with multi-component potential functions can be generated, whose Hamiltonian structures can be worked out by the variational identity. As application illustrations, two integrable Hamiltonian hierarchies with 4 component potential functions are obtained, respectively, some new reduced equations are followed to present. Specially remark that the integrable hierarchies obtained by taking use of the approach presented in the paper are not integrable couplings. Finally, we generalize an equation obtained in the paper to introduce a general nonlinear integrable equation with variable coefficients whose bilinear form, BEcklund transformation, Lax pair and infinite conserved laws are worked out, respectively, by taking use of the Bell polynomials.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0553-1