Bifurcation decay modes

A quantum mechanical proof of the bifurcation of the decay modes is... 

When Da < 1, all the modes in the sum decay in time towards the C = 0 state, but for Da > 1 at least the mode with n = 0 grows, and (7 = 0 becomes unstable to small localized perturbations. To obtain a nonlinear approximation of the steady filament solution close to the bifurcation point Dac = 1, a perturbation approximation can be used by introducing... 

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