The trajectories of particles in Stokes waves

By Adrian Constantin. 2006

802 citations recorded by the source corpus.

Subfields: Computational Mechanics, Earth-Surface Processes, Oceanography

View Paper: https://www.semanticscholar.org/paper/1ea01c9e07ed8481092f29d08c2e7edf941d2337

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Citations in the corpus

The Cauchy problem for the Novikov equation (2012, neutral): “[4–6,16].”
Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation (2009, background): “Such properties made it possible to describe the particle motion beneath irrotational waves [8, 14] and the exploration of this aspect for flows with constant vorticity is now plausible.”
On Gerstner’s Water Wave (2008, background): “In recent years there has been growing interest in free surface water waves (see [1, 2, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 18, 20, 21, 22, 25, 35, 36]), but the current state of affairs regarding explicit solutions has not advanced much since the last century.”
Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems (2016, neutral): “properties for CH type and related nonlinear evolution equations, we refer the reader to [12], [13], [11], [15], [16], [6], [23], [49], [53], [50], [17], [45], [8], [42], [43], [44], [4], [3], [64], [18], [5], [47], [48], [10], [9], [70], and the references therein.”
A three-component generalization of Camassa–Holm equation with N-peakon solutions (2011, background): “The peakons replicate a feature that is characteristic for the waves of great height – waves of largest amplitude that are exact solutions of the governing equations for water waves [11,41,12].”
On the Cauchy problem for the two-component Camassa–Holm system (2011, neutral): “the discussion in [10,12,27,29].”
Well-posedness and blow-up solution for a modified two-component periodic Camassa–Holm system with peakons (2010, background): “The peakons replicate a feature that is characteristic for the waves of great height-waves of the largest amplitude that are exact solutions of the governing equations for water waves [12,17,22,49].”
Some Nonlinear, Equatorially Trapped, Nonhydrostatic Internal Geophysical Waves (2014, methodology): “An explicit, nonlinear solution for equatorial ocean waves propagating eastward, in the layer above the thermocline and beneath the near-surface layer in which wind effects are noticeable, was recently described in Constantin (2013). The solution was obtained in Lagrangian coordinates by adapting to”