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

Yufeng Zhang, Honwah Tam and Wei Jiang

Chaos, Solitons & Fractals, 2008, vol. 36, issue 2, 271-277

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.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:36:y:2008:i:2:p:271-277

DOI: 10.1016/j.chaos.2006.06.030

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