In this paper, by means of symmetric constraint, a new integrable systemis obtained, and the relation between the system and the following eigenvalueproblemis discussed. Furthermore, the representation of the solution for Levy equationis given.
In this paper, the Broer- Kaup equation[￣1,2,3] and its hierarchy are discussed. Further, using the nonlinearization￣[4] of Lax pairs for the soliton equation, by means of the complex form of real standard symplectic construction, two complex finite dimensional Liouville completely integrable systems associated with Broer-Kaup hierarchy are obtained.So, the solutions of Broer-Kaup hierarchy are transformed into the solutions of Hamiltonian equations
