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A simple method for generating integrable hierarchies with multi-potential functions. (English) Zbl 1092.37044

Summary: A simple efficient method for obtaining integrable hierarchies of evolution equations with multi-potential functions is proposed. By making use of the concept of cycled numbers, a new loop algebra \(\widetilde A_{1}^*\) is constructed. Taking in account of applicable convenience, a few subalgebras of the loop algebra \(\widetilde A_{1}^*\) are presented again, from one of them, two new integrable Hamiltonian hierarchies with multi-potential functions are obtained. Finally, a \(3\times 3\) loop algebra \(\widetilde G\) with five dimensions is established, from which a coupled integrable coupling system of one of the above integrable hierarchies is derived. The approach presented in this paper can be used generally.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K30 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
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