Abstract: We make use of the K-dv equation to clarify the relation-shios among the five characteristics for a class of nonlinear wave equatioos.It is shown that (1) Inverse scatering transform (IST);(2) Böcklund transformation (BT);(3)N-soliton solutions (N-SS);(4)a unite or an infinite number of conservation laws (CL) and (5)a complete integrable Hamilton system (HS) are closely related.The scheme of the presentation is shown in the following figure