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New integrable couplings of the Tu hierarchy with self-consistent sources. (Chinese. English summary) Zbl 1274.35314

Summary: A new isospectral problem is firstly presented, then we derive an integrable system of soliton hierarchy. Also we obtain new integrable couplings of the Tu soliton equation hierarchy with self-consistent sources associated with loop algebra \(\widetilde{sl}(4)\). In this paper, we also point out that there exist some errors in Yu’s paper and correct these errors and set up a new formula. The method can be generalized to other soliton hierarchies with self-consistent sources.

MSC:

35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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