Nonlinear Dispersive Waves

This volume explores a number of exciting developments in the field of nonlinear dispersive waves with a particular focus on waves arising in the ocean. Chapters are based on talks given at the workshop Nonlinear Dispersive Waves that was held at University College Cork, Ireland, on April 24-25, 2023. Specific topics covered include:

• The recovery of steady rotational wave surface profiles;
• Hamiltonian models for the propagation of long gravity waves;
• Waves propagating at the surface of a fluid covered by floating ice plates;
• The use of spherical coordinates to describe arctic ocean waves;

• Boundary value problems related to the Muskat Problem.
  Nonlinear Dispersive Waves will appeal to researchers as well as graduate students interested in this active area of research.

  Explores developments in nonlinear dispersive waves with a focus on waves arising in the ocean Features cutting-edge research from leaders in a variety of areas within pure and applied mathematics Collects chapters based on talks from the workshop Nonlinear Dispersive Waves held at University College Cork in 2023

  Autorentext

  David Henry is a mathematician whose research interests comprise the analysis of nonlinear partial differential equations, and free-boundary problems, with a particular interest in the mathematical theory of water waves. Aside from several visiting researcher positions abroad, David has been based in Ireland since obtaining his PhD in mathematics from Trinity College Dublin in 2008. He currently leads a research group at University College Cork.

  Inhalt

Preface.- BOUNDARY VALUE PROBLEMS RELATED TO THE MUSKAT PROBLEM.- SOME FLOW CHARACTERISTICS OF STOKES WAVES VIA COMPLEX ANALYSIS.- RECOVERY OF TRAVELING WATER WAVES WITH SMOOTH VORTICITY FROM THE HORIZONTAL VELOCITY ON A LINE OF SYMMETRY FOR VARIOUS WAVE REGIMES.- NUMERICAL COMPUTATION OF STEADY ROTATIONAL WAVES AND RECOVERY OF THE SURFACE PROFILE FROM BOTTOM PRESSURE MEASUREMENTS.- Hamiltonian models for the propagation of long gravity waves, higher-order KdV-type equations and integrability.- An introduction to the Zakharov equation for modelling deep water waves.- Rotating convection and flows with horizontal kinetic energy backscatter.- Flexural-gravity waves under ice plates and related flows.- Nonlinear water waves and wave-current interactions at arbitrary latitude.- HOLLOW VORTICES AS NONLINEAR WAVES.- SPHERICAL COORDINATES FOR ARCTIC OCEAN FLOWS.