APPROXIMATE ANALYTICAL SOLUTIONS FOR SOME STRONGLY NONLINEAR PROBLEMS

<正> In this paper, some problems of strongly nonlinear oscillations and waves are analyzed by using the modified method of full approximation developed by the authors. Firstly, a class of strongly nonlinear oscillation systems is studied and, in particular, for the modified van der Pol oscillator, the second-order expression of its limit cycle solution is quite straightforwardly found out, which agrees with the results obtained by way of the generalized method of averaging in Ref. [1]. Then for the modified KdV equation, the correct secondorder appoximate solution of solitary waves is given. Finally, for the generalized KdV equation with a fifth-order dispersion term, the third-order asymptotic solution of solitary waves is derived and the form of oscillatory solitary waves is analytically given. All the results show that the modified method of full approximation can be effectively applied to the investigation of some mathematical problems with strong nonlinearity.