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A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with $\stackrel{˜}{sl}\left(4\right)$. (English) Zbl 1225.35193
Summary: A kind of integrable couplings of soliton equations hierarchy with self-consistent sources associated with $\stackrel{˜}{sl}\left(4\right)$ is presented. As an application example, the hierarchy of Yang equations with self-consistent sources is derived. Furthermore, we construct an integrable couplings of the Yang soliton hierarchy with self-consistent sources by using of the loop algebra $\stackrel{˜}{sl}\left(4\right)$.
##### MSC:
 35Q51 Soliton-like equations 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies 35C08 Soliton solutions of PDE 22E70 Applications of Lie groups to physics; explicit representations