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math.AP2021
Rigorous justification of the Whitham modulation equations for equations of Whitham-type
William A. Clarke, Robert Marangell, Wesley R. Perkins
We prove that the modulational instability criterion of the formal Whitham modulation theory agrees with the spectral stability of long wavelength perturbations of periodic travell…
math.AP2020★ 4 cited
A new Evans function for quasi-periodic solutions of the linearised sine-Gordon equation
William A. Clarke, Robert Marangell
We construct a new Evans function for quasi-periodic solutions to the linearisation of the sine-Gordon equation about a periodic travelling wave. This Evans function is written in…