Nearly real fronts in a Ginzburg-Landau equation
Proceedings of the Royal Society Edinburgh
Subcritical fronts are shown to exist in a quintic version of the well-known complex Ginzburg–Landau equation, which has a subcritical pitchfork as well as a supercritical saddle-node bifurcation. The fronts connect a finite amplitude plane wave state to a stable zero solution. The unstable manifold at finite amplitude and stable manifold of vanishing amplitude solutions are shown to intersect transversely on an invariant zero-wavenumber manifold with parameters set to be real. By the persistence of transverse intersection, frontal connections exist for a continuum of nearly real fronts parametrised by appropriate variables that exhibit some interesting changes in dimension.
C.K.R.T. Jones, T.M. Kapitula and J. Powell. “Nearly real fronts in a Ginzburg-Landau equation,’ Proc. Roy. Soc. Edinburgh 116A, 193–206, 1990.