Whitham modulation theory for generalized Whitham equations and a general criterion for modulational instability
Adam L. Binswanger,
Mark A. Hoefer,
Boaz Ilan
et al.
Abstract:The Whitham equation was proposed as a model for surface water waves that combines the quadratic flux nonlinearity f (u) = 1 2 u 2 of the Korteweg-de Vries equation and the full linear dispersion relation Ω(k) = √ k tanh k of uni-directional gravity water waves in suitably scaled variables. This paper proposes and analyzes a generalization of Whitham's model to unidirectional nonlinear wave equations consisting of a general nonlinear flux function f (u) and a general linear dispersion relation Ω(k). Assuming t… Show more
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