Travelling waves bifurcation of the modified Ginzburg-Landau's equation

The main target of this work is the modified Ginzburg-Landau's equation, addresses given in a monograph of G. G. Malinetskii as one of the equations, where blow-up regimes can be possible. Together with periodic boundary conditions this equation forms a boundary value problem. Existence, stability-instability and local bifurcations are the main purposes of this work. It has been shown that in this aspect the results are those that obtained while considering the traditional version of Ginzburg-Landau's equation.
The study of bifurcation problem is based on the method of normal forms and adapted to the assigned boundary value problem.