PHASE DYNAMICS AND LOCALIZED SOLUTIONS TO THE GINZBURG-LANDAU TYPE AMPLITUDE EQUATIONS

We study different types of long wavelength phase modulation and localized modes in the dissipative media described by the Ginzburg-Landau type amplitude equations. We derive nonlinear phase equations for the phase instabilities and investigate their behaviors. When the phase description breaks down, phase slip process occurs and topologically different states come out. In a certain parameter range localized solutions or solitonlike solutions appear as stable solutions to the amplitude equations.