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Two New Integrable Hierarchies and Their Nonlinear Integrable Couplings

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Document pages: 17 pages

Abstract: By introducing an invertible linear transform, a newLie 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 hierarchyare achieved by using the trace identity or the variational identity. Then, twospecial non-semisimple Lie algebras  and  are explicitlyconducted. As an application, the nonlinear continuous integrable couplings ofthe obtained integrable systems as well as their bi-Hamiltonian structures areestablished, respectively.

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