Envelope equations for modulated non-conservative waves
Biktashev, Vadim N.
In many applications people deal with waves that are locally plane and periodic, but at large distances and/or over long intervals if time change their characteristics, i.e. modulated waves. 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. The purpose of the present paper is to review results of a particular approach of this kind, which is free from these disadvantages. This approach is mostly 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.