Breakdown of the Whitham Modulation Theory and the Emergence of Dispersion
Thomas J. Bridges
Source abstract
The Whitham modulation theory for periodic traveling waves of PDEs generated by a Lagrangian produces first‐order dispersionless PDEs that are, generically, either hyperbolic or elliptic. In this paper, degeneracy of the Whitham equations is considered where one of the characteristic speeds is zero. In this case, the Whitham equations are no longer valid. Reformulation and rescaling show that conservation of wave action morphs into the Korteweg–de Vries (KdV) equation on a longer time scale thereby generating dispersion in the Whitham modulation equations even for finite amplitude waves.
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