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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 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.Comment: 11 pages, 3 figure