On the principal bifurcation branch of a third-order nonlinear long-wave equation

We study the principal bifurcation curve of a third-order equation which describes the nonlinear evolution of several systems with a long-wavelength instability. We show that the main bifurcation branch can be derived from a variational principle. This allows us to obtain a close estimate of the complete branch. In particular, when the bifurcation is subcritical, the large amplitude stable branch can be found in a simple manner.