In this paper, the normalized nonlinear Schrodinger equation with amplifiers gain in lumped amplifiers picosecond soliton system is solved by means of the travelling-wave method and the approximate analytical solution is derived. At the same time general equations for the evolution of ampititude, center position, phase are derived. Moreover, the soliton stability in lumped amplifiers picosecond soliton system is discussed by the approximate analytical solution and general equations for the evolution of ampititude, center position, phase, and the result is that the soliton can keep stable in lumped amplifiers picosecond soliton system.