An afternoon on 2D and 3D solitary waves and lumps with oscillatory tails

F9.largeTuesday afternoon, 15 July, had three talks on gravity-capillary solitary waves and lumps, and related solutions when an elastic sheet is present, or density stratification.  Emilian Parau started with a presentation of results on four settings with similar types of travelling waves: stratified fluids, 2D gravity capillary, 3D gravity capillary, and the case where an elastic plate (e.g. ice sheet) covers the surface. Zhan Wang contrasted the solutions of the elliptic 2+1 NLS equation to solutions of the full Euler equation.  Stability was tested by running an initial-value code, by adding perturbations to the solitary waves as initial conditions.  Results include the breakup of 3D multi-pulse solitary waves into a finite set of smaller localised states.  In the above two talks the waves were symmetric.  In the third talk, Jean-Marc Vanden-Broeck presented results showing the existence of non-symmetric solitary waves in both 2D and 3D.  In 2D the non-symmetric waves were solutions of the Euler equations whereas the 3D waves were solutions of a model equation.  Videos for the three talks are available here (Parau), here (Wang), and here (Vanden-Broeck).

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