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Starting from a Tu Guizhang‘s isospectral‘problem, a Lax pair is obtained by means of Tu scheme ( we call it Tu Lax pair ). By applying a gauge transformation between matrices, the Tu Lax pair is changed to its equivalent Lax pair with the traces of spectral matrices being zero, whose compatibility gives rise to a type of Tu hierarchy of equations. By making use of a high order loop algebra constructed by us, an integrable coupling system of the Tu hierarchy of equations are presented. Especially, as reduction cases, the integrable couplings of the celebrated AKNS hierarchy, TD hierarchy and Levi hierarchy are given at the same time. 相似文献
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The Liouville integrable coupling system of the m-AKNS hierarchy and its Hamiltonian structure 下载免费PDF全文
In this paper a type of 9-dimensional vector loop algebra \tilde{F}
is constructed, which is devoted to establish an isospectral problem.
It follows that a Liouville integrable coupling system of the m-AKNS
hierarchy is obtained by employing the Tu scheme, whose Hamiltonian
structure is worked out by making use of constructed quadratic
identity. The method given in the paper can be used to obtain many
other integrable couplings and their Hamiltonian structures. 相似文献
3.
In general, Liouville integrable hierarchies of evolution equations were obtained by choosing proper U in zero curvature frame Ut - Vx + [U, V] = 0 first. But in the present paper, a new Liouville integrable hierarchy possessing bi-Hamiltonian structure is obtained by choosing V with derivatives in x and spectral potentials. Then integrable coupling, i.e. expanding Lax integrable model of the hierarchy obtained is presented by constructing a subalgebra of loop algebra A2. 相似文献
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