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Erschienen in:
1988 | OriginalPaper | Buchkapitel
Bifurcation and Permanent Gravitational Waves
verfasst von : Eberhard Zeidler
Erschienen in: Nonlinear Functional Analysis and its Applications
Verlag: Springer New York
Enthalten in: Professional Book Archive
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In this chapter we study the existence of nontrivial water waves in a channel of finite depth. As shown in Figure 71.1 we find that, in addition to the trivial parallel flow, there occur nontrivial wave motions at certain critical velocities c. Such waves were studied during the nineteenth century by British hydro-dynamicists such as Airy, Stokes, Kelvin, and Rayleigh. They solved the linearized problems and calculated nonlinear approximations up to order 6. No convergence proofs, however, were given.