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Secondary criticality of water waves. Part 2. Unsteadiness and the Benjamin–Feir instability from the viewpoint of hydraulics
Published online by Cambridge University Press: 28 September 2006
Abstract
The theory for criticality presented in Part 1 is extended to the unsteady problem, and a new formulation of the Benjamin–Feir instability for Stokes waves in finite depth coupled to a mean flow, which takes the criticality matrix as an organizing centre, is presented. The generation of unsteady dark solitary waves at points of stability changes and their connection with the steady dark solitary waves of Part 1 are also discussed.
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