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We study the principal bifurcation curve of a third order equation whichdescribes the nonlinear evolution of several systems with a long--wavelengthinstability. We show that the main bifurcation branch can be derived from avariational principle. This allows to obtain a close estimate of the completebranch. In particular, when the bifurcation is subcritical, the large amplitudestable branch can be found in a simple manner.Comment: 11 pages, 3 figure

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