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Bifurcation and Permanent Gravitational Waves

In: Nonlinear Functional Analysis and its Applications

Author

Listed:
  • Eberhard Zeidler

    (Max-Planck-Institut für Mathematik in den Naturwissenschaften)

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.

Suggested Citation

  • Eberhard Zeidler, 1988. "Bifurcation and Permanent Gravitational Waves," Springer Books, in: Nonlinear Functional Analysis and its Applications, chapter 0, pages 448-478, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4566-7_15
    DOI: 10.1007/978-1-4612-4566-7_15
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