Abstract: This paper reports a type of laws which governs action potential of nervous impulses,and it is discussed by general form-nonlinear dispersive process. We find that the nervous wave is a slowly varying amplitude solitary wave in the small dispersive case. He prove that the solitary wave is not generated in the ordinary dispersion,but a travelling wave with varying amplitudes may be obtained. The stability of various possible action potentials and bifurcation in overdamped case are also discussed in this paper.