Sideband Instability of Waves with Periodic Boundary Conditions
The sideband instability for traveling waves is studied experimentally under periodic boundary conditions. Such an instability, known as the Eckhaus instability , is subcriticai in the case of stationary patterns. In contrast, for traveling waves, we show that the instability occurs via a forward bifurcation. This enables the study of the development of the phase instability and the change in wavenumber. We analyze the phase equation describing this instability. We show that the bifurcation is indeed supercritical. It is characterized by soliton solutions at onset and a transition to phase turbulence away from onset.
KeywordsRayleigh Number Soliton Solution Phase Equation Stationary Pattern Pure Mode
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