A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension

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Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity–capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as ‘lumps’), and a mathematically rigorous existence theory for strong surface tension (Bond number (Formula presented.) greater than (Formula presented.)) has recently been given. In this article we present an existence theory for the physically more realistic case (Formula presented.). A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey–Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.


Enheter & grupper
Externa organisationer
  • Swiss Federal Institute of Technology
  • Saarland University
  • Loughborough University

Ämnesklassifikation (UKÄ) – OBLIGATORISK

  • Matematisk analys
Sidor (från-till)773-820
TidskriftArchive for Rational Mechanics and Analysis
Tidigt onlinedatum2017 dec 9
StatusPublished - 2018
Peer review utfördJa