Abstract
A nonlinear evolution equation is considered which is often encountered in modelling the behaviour of perturbations in various active dissipative media, e.g. in problems of fluid film flow hydrodynamics. Wave solutions regular in space and both periodical and quasi-periodical in time generating from steady-state and steady-state travelling waves have been found numerically. Stability of some solutions has been investigated and bifurcation analysis has been carried out. The analysis has demonstrated that there is a sequence of bifurcations of solutions stable with respect to disturbances of the same spatial period and it has been shown that the bifurcations are related to the loss of some symmetries of the initial solution. It is also shown that the regions of “quiet” time behaviour and those of intensive variations are separated in the temporal period of solutions with the bifurcation parameter increasing.
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