Abstract
Exact solutions of some non-linear hydrodynamic equations containing a small parameter are obtained by means of the differential perturbation technique proposed by the authors.
Several important conceptions associated with the differential perturbation technique, such as the degree of non-linearity and the existence condition of exact solutions, are specified in connection with the differential perturbation. The condition that a non-linear equation with a small parameter is transformed into a linear equation with a small parameter is transformed into a linear one by means of this technique is also obtained.
The Cole-Hopf transformation is obtained for the Burgers equation, if the degree of nonlinearity is estimated by examining the equation. Under the similar assumption, an exact solution of the K-dV equation is obtained. This result is parallel with the D-operator procedure proposed by Hirota.
As the last example, a non-linear equation which has a singularity regarding with the small parameter is solved as the parallel application with the PLK method.
