TITLE:
Two New Integrable Hierarchies and Their Nonlinear Integrable Couplings
AUTHORS:
Hui Chang, Yuxia Li
KEYWORDS:
Non-Semisimple Lie algebra, Nonlinear Integrable Coupling, Hamiltonian Structure, Trace Identity, Variational Identity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.6,
June
28,
2018
ABSTRACT: By introducing an invertible linear transform, a new
Lie algebra G is obtained from the Lie algebra H.
Making use of the compatibility conditions of the respective isospectral problems, a generalized NLS-MKdV hierarchy and a new integrable soliton hierarchy
are achieved by using the trace identity or the variational identity. Then, two
special non-semisimple Lie algebras and are explicitly
conducted. As an application, the nonlinear continuous integrable couplings of
the obtained integrable systems as well as their bi-Hamiltonian structures are
established, respectively.