4. Modeling of the KdV equation and its solution

Even though the KdV equation can be derived by using either the approximation method of series expansion or the approximation method of harmonics expansion, in the process of symbolic manipulation there appear quadratic evolutionary models. These models appear simultaneously in the first and the second derivatives which causes contradictions in the model building. Based on this understanding, the KdV equation, established by using series expansion or harmonics expansion, needs to be restudied. Also, due to the fact that this model contains a quadratic terms of the second derivative, the analytical solution of the solitary waves can only be a special case under local conditions, whose general characteristics should contain the blown‐up problem of unintegrability. At the same time, in this paper, we consider the general characteristics of Burgers equation.