Abstract: This paper presents a generalized form of the method of full approximation. By using the concept of asymptotic linearization and making the coordinate transformations including the nonlinear functionals of dependent variables, the original nonlinear problems are linearized and their higher-order solutions are given in terms of the first-term asymptotic solutions and corresponding transformations. The analysis of a model equation and some problems of weakly nonlinear oscillations and waves with the generalized method shows that it is effective and straightforward.

Key words: perturbation methods, methods of full approximation, asymptotic linearization, nonlinear waves, nonlinear oscillations