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Reduced equations of the self-dual Yang–Mills equations and applications

Author

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  • Zhang, Yufeng
  • Tam, Honwah
  • Jiang, Wei

Abstract

A few reduced equations from the self-dual Yang–Mills equations are presented, which are seemly extended zero curvature equations. As their applications, a good many nonlinear evolution equations could be obtained. In this paper, a (2+1)-dimensional AKNS hierarchy of soliton equations is generated from one of reduced equations of the self-dual Yang–Mills equations. With the help of a proper loop algebra, the Hamiltonian structure of its expanding integrable model (actually, its integrable couplings) is worked out by using the quadratic-form identity, which is Liouville integrable. The way presented in the paper has extensive applications. That is to say, making use of the approach specially a few higher-dimensional zero curvature equations in the paper could produce a lots of higher-dimensional integrable coupling systems and their corresponding Hamiltonian structures.

Suggested Citation

  • Zhang, Yufeng & Tam, Honwah & Jiang, Wei, 2008. "Reduced equations of the self-dual Yang–Mills equations and applications," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 271-277.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:2:p:271-277
    DOI: 10.1016/j.chaos.2006.06.030
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