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A host of traveling waves in a model of three-dimensional water-wave dynamics

Robert L. Pego·Jose Raul Quintero
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Abstract

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.

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Robert L. Pego, Jose Raul Quintero. 2001-11-20. A host of traveling waves in a model of three-dimensional water-wave dynamics. https://doi.org/10.1007/s00332-001-0478-5

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