For general amplitude periodic traveling waves of the Ostrovsky equation, strict hyperbolicity of the derived Whitham system implies spectral modulational stability near the origin, while ellipticity implies spectral instability.
Baumg¨ artel.Analytic perturbation theory for matrices and operators, volume 15 of Operator Theory: Advances and Applications
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On the Modulation of Wave Trains in the Ostrovsky Equation
For general amplitude periodic traveling waves of the Ostrovsky equation, strict hyperbolicity of the derived Whitham system implies spectral modulational stability near the origin, while ellipticity implies spectral instability.