One type of variability that is ubiquitous among luminous blue stars is that associated with their massive stellar winds. Ultraviolet spectral lines show variable narrow absorption components that may arise from dense shells or clumps in the wind; the observed soft X-ray and non-thermal radio emission from these stars may be produced in embedded wind shocks associated with these shells. The line-driving of such winds is known to be strongly unstable, and recent numerical simulations of the dynamical, nonlinear evolution of such instabilities indicate that such shocks and dense shells do indeed form (Owocki, Castor, and Rybicki 1988; hereafter OCR). However, the structure computed in these dynamical simulations is quite different, and in some sense opposite, what was anticipated in earlier heuristic shock models (e.g. Lucy 1984, Krolik and Raymond 1985, Abbott 1988); the highest speed material is veryrarefied, not dense, and the strongest shocks that form are of thereverse, not forward, type. In subsequent simulations we have found that the detailed character of this structure can depend on many variables, but this tendency always to form high speed rarefied waves and reverse shocks is quite robust. It is thus important that we have a clear understanding of the reasons for this tendency, and it is on this point that we focus our comments here.
Integrable nonlinear evolution equations with time‐dependent coefficients