Abstract: Based on a 2 × 2 eigenvalue problem, a set of (1 + 1)-dimensional soliton equations are proposed. Moreover, we obtain a finite dimensional Hamilton system with the help of nonlinearization approach. Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system, hence, we can verify it is completely integrable in Liouville sense.

Key words: (1+1)-dimension equation, Hamilton system, the generating function