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. Periodic steady-state travelling solutions have been found numerically for it. Stability of these solutions has been investigated and bifurcation analysis has been carried out. The analysis has demonstrated that decrease of the wave number causes more and more new families of steady-state travelling solutions. A countable set of such solutions is formed in the limit when the wave number tends to zero. It is also shown that time-oscillating solutions can be generated from steady-state ones due to bifurcation of the Landau-Hopf type.
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