Groves M.D., Haragus M.'s A Bifurcation Theory for Three-Dimensional Oblique PDF

By Groves M.D., Haragus M.

This text provides a rigorous life thought for small-amplitude threedimensional vacationing water waves. The hydrodynamic challenge is formulated as an infinite-dimensional Hamiltonian procedure within which an arbitrary horizontal spatial path is the timelike variable. Wave motions which are periodic in a moment, varied horizontal path are detected utilizing a centre-manifold relief method in which the matter is diminished to a in the neighborhood identical Hamiltonian process with a finite variety of levels of freedom.

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

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A multiplicity result for solitary gravity-capillary waves in deep water via critical-point theory. Arch. Ratl. Mech. Anal. 146, 183–220. , GROVES, M. , AND TOLAND, J. F. 1996. A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers. Phil. Trans. Roy. Soc. London A 354, 575–607. , AND NICHOLLS, D. P. 2000. Traveling two and three dimensional capillary gravity water waves. SIAM J. Math. Anal. 32, 323–359. -C. 1997. Solitary waves of generalized Kadomtsev-Petviashvili equations.

1991. Hamiltonian and Lagrangian Flows on Center Manifolds. Berlin: SpringerVerlag. [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.

25] MIELKE, A. 1991. Hamiltonian and Lagrangian Flows on Center Manifolds. Berlin: SpringerVerlag. [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.

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A Bifurcation Theory for Three-Dimensional Oblique Travelling Gravity-Capillary Water Waves by Groves M.D., Haragus M.


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