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has been cited by the following article:

• 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.