Numerical computations of two-dimensional flexural-gravity solitary waves on water of arbitrary depth

Tao Gao, Jean-Marc Vanden-Broeck, Zhan Wang

Research output: Contribution to journalArticle

5 Citations (Scopus)
22 Downloads (Pure)


This work is concerned with flexural-gravity solitary waves on water of finite depth. The deformation of the elastic sheet is modelled based on the Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypotheses. Both steady and unsteady waves are computed numerically for the full Euler equations by using a conformal mapping technique. Complete bifurcation diagrams of solitary waves are presented, and various dynamical experiments, including the evolution of unstable solitary waves and the generation of stable ones, are carried out via direct time-dependent simulations. In particular, we show that generalized solitary waves can also be excited by moving loads on the elastic cover.

Original languageEnglish
Pages (from-to)436-450
Number of pages15
JournalIMA Journal of Applied Mathematics
Issue number3
Early online date22 Mar 2018
Publication statusPublished - 1 Jun 2018


  • Solitary waves
  • Wave interactions
  • Gravity waves

Cite this