Download A Bifurcation Theory for Three-Dimensional Oblique by Groves M.D., Haragus M. PDF

By Groves M.D., Haragus M.

This text provides a rigorous lifestyles conception for small-amplitude threedimensional traveling water waves. The hydrodynamic challenge is formulated as an infinite-dimensional Hamiltonian method during which an arbitrary horizontal spatial course is the timelike variable. Wave motions which are periodic in a moment, diversified horizontal course are detected utilizing a centre-manifold aid approach in which the matter is diminished to a in the community an identical Hamiltonian method with a finite variety of levels of freedom.

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Extra resources for A Bifurcation Theory for Three-Dimensional Oblique Travelling Gravity-Capillary Water Waves

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1999. Nonlinear gravity and capillary-gravity waves. Ann. Rev. Fluid Mech. 31, 301–346. [9] DUISTERMAAT, J. J. 1984. Bifurcation of periodic solutions near equilibrium points of Hamiltonian systems. In Lecture Notes in Mathematics 1057—Bifurcation Theory and Applications, Montecatini 1983 (ed. ), pages 57–105. New York: Springer-Verlag. [10] GROVES, M. D. 2001. An existence theory for three-dimensional periodic travelling gravitycapillary water waves with bounded transverse profiles. Physica D 152–153, 395–415.

Phil. Mag. 29, 688–700.

26] MOSER, J. 1976. Periodic orbits near an equilibrium and a theorem by Alan Weinstein. Commun. Pure Appl. Math. 29, 727–747. [27] PEGO, R. , AND QUINTERO, J. 2002. A host of traveling waves in a model of threedimensional water-wave dynamics. J. Nonlinear Sci. 12, 59–83. [28] PLOTNIKOV, P. I. 1980. Solvability of the problem of spatial gravitational waves on the surface of an ideal fluid. Sov. Phys. Dokl. 25, 170–171. , AND SHINBROT, M. 1981. Three-dimensional nonlinear wave interaction in water of constant depth.

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