This paper addresses the singular 1-soliton solution of the K(m, n) equation that is being considered with generalized evolution. The ansatz method will be used to extract the singular 1-soliton solution of this equation. A couple of constraint conditions will fall out in order for the singular soliton solutions to exist. Subsequently, the special cases of this equation will be studied. They are the KdV and the mKdV equations where the extended (G'/G)-expansion method will be employed to extract a few non-linear wave solutions.