Bifurcation and Permanent Gravitational Waves

Eberhard Zeidler
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Eberhard Zeidler: Max-Planck-Institut für Mathematik in den Naturwissenschaften

Chapter Chapter 71 in Nonlinear Functional Analysis and its Applications, 1988, pp 448-478 from Springer

Abstract: Abstract 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.

Keywords: Solitary Wave; Operator Equation; Critical Velocity; Sinusoidal Wave; Circular Ring (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-4566-7_15

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DOI: 10.1007/978-1-4612-4566-7_15

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