  A method for finding exact solutions of nonlinear differential equations is
presented. Our method is based on the application of the Newton polygons
corresponding to nonlinear differential equations. It allows one to express
exact solutions of the equation studied through solutions of another equation
using properties of the basic equation itself. The ideas of power geometry are
used and developed. Our approach has a pictorial rendition, which is is
illustrative and effective. The method can be also applied for finding
transformations between solutions of the differential equations. To demonstrate
the method application exact solutions of several equations are found. These
equations are: the Korteveg - de Vries - Burgers equation, the generalized
Kuramoto - Sivashinsky equation, the fourth - order nonlinear evolution
equation, the fifth - order Korteveg - de Vries equation, the modified Korteveg
- de Vries equation of the fifth order and nonlinear evolution equation of the
sixth order for the turbulence description. Some new exact solutions of
nonlinear evolution equations are given.
