Vadim N. Biktashev
(presented at an IUTAM symposium in Liverpool, July 2002)
Modulated waves, i.e. waves that are locally plane and periodic, but at large distances and/or over long intervals of time change their characteristics, appear in many applications. An efficient way to study such waves is the method of envelope equations, when the original wave equations are replaced by equations describing the slowly varying parameters of the waves. The practical approaches to this problem are numerous; however, many of them have limitations, either in achievable accuracy, or in the wave equations to which they could apply (e.g. only conservative systems), or both. In this paper we discuss an approach of this kind, which appear to be free from these disadvantages. This approach is illustrated for autowaves, which, in the author's opinion, should play the same role in the theory of waves, as auto-oscillations=limit cycles play in the theory of oscillations: as the basic, least degenerate type of solutions.
postscript (737K)