Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2001-11-20
Nonlinear Sciences
Pattern Formation and Solitons
22 pages with 1 figure, LaTeX2e with amsfonts, epsfig packages
Scientific paper
We describe traveling waves in a basic model for three-dimensional water-wave dynamics in the weakly nonlinear long-wave regime. Small solutions that are periodic in the direction of translation (or orthogonal to it) form an infinite-dimensional family. We characterize these solutions through spatial dynamics, by reducing a linearly ill-posed mixed-type initial-value problem to a center manifold of infinite dimension and codimension. A unique global solution exists for arbitrary small initial data for the two-component bottom velocity, specified along a single line in the direction of translation (or orthogonal to it). A dispersive, nonlocal, nonlinear wave equation governs the spatial evolution of bottom velocity.
Pego Robert L.
Quintero José Raúl
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