A Survey of Numerical Method for Solitary Waves(Ⅰ)

Abstract:

      This paper is devoted to introduce the history of numerical study of solitons and the main results for K. D. V. equation, R. L. W. equation, Klein-Gordon equation, Sine-Gordon equation and so on.The technique for constructing difference schemes based on conservation and characteristic is discussed. The two main methods for analysis of stability is given too. Then several finite element methods are discussed. The final part of this paper is for various-spectral methods.