Abstract
Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of Yang hierarchy were obtained.
Highlights
With the development of soliton theory, super integrable systems associated with Lie superalgebra have aroused growing attentions by many mathematicians and physicists
Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed
A few approaches to construct linear integrable couplings of the classical soliton equation are presented by permutation, enlarging spectral problem, using matrix Lie algebra [12] constructing new loop Lie algebra and creating semi-direct sums of Lie algebra
Summary
With the development of soliton theory, super integrable systems associated with Lie superalgebra have aroused growing attentions by many mathematicians and physicists. There are some interesting results on the super integrable systems, such as Darboux transformation [5], super Hamiltonian structures in [6] [7], binary nonlinearization [8] and reciprocal transformation [9] and so on. Inspired by Zhang [13] and You [14], we hope to construct nonlinear super integrable couplings of the super Yang hierarchy through enlarging matrix Lie super algebra. Based on the enlarged Lie super algebra sl (4 | 1) , we work out nonlinear super integrable Hamiltonian couplings of the super Yang hierarchy. We will reduce the nonlinear super Yang integrable Hamiltonian couplings to some special cases
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