Rigorous justification of the Whitham modulation equations for equations of Whitham type

  title={Rigorous justification of the Whitham modulation equations for equations of Whitham type},
  author={W. A. Clarke and Robert Marangell and Wesley R. Perkins},
  journal={Studies in Applied Mathematics},
We prove that the modulational instability criterion of the formal Whitham modulation theory agrees with the spectral stability of long wavelength perturbations of periodic travelling wave solutions to the generalized Whitham equation. We use the standard WKB procedure to derive a quasi-linear system of three Whitham modulation equations, written in terms of the mass, momentum, and wave number of a periodic travelling wave solution. We use the same quantities as parameters in a rigorous… 


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