Linear and nonlinear waves
Citations
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Cites background or methods from "Linear and nonlinear waves"
...If this were the case, the boundedness of the wave height in combination with an unbounded slope captures the main features of a breaking wave [33]....
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...Another development of models for water waves was initiated in order to gain insight into wave breaking, one of the most fundamental aspects of water waves for which there appears to be no satisfactory mathematical theory [33]....
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...To remedy this shortcoming of the KdV equation Whitham proposed to formally replace the dispersive term uxxx by a convolution with a singular function chosen so that the newly obtained equation presents wave breaking (see [18, 33])....
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...[33]: the solution remains bounded but its slope becomes unbounded....
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...Starting from the observation that the strong dispersive effect incorporated into the KdV model prevents wave breaking, Whitham (see the discussion in [33]) initiated the quest for equations that are simpler than the governing equations for water waves and which could model breaking waves....
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829 citations
Cites background from "Linear and nonlinear waves"
...Originally this approach was designed for the study of waves in continuous media — some older papers also use the term Benjamin-Feir instability instead [402]....
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596 citations
References
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