Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

Denys Dutykh, Mark Hoefer, Dimitrios Mitsotakis

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge–Kutta method of order 4.

Original languageBritish English
Pages (from-to)371-397
Number of pages27
JournalTheoretical and Computational Fluid Dynamics
Volume32
Issue number3
DOIs
StatePublished - 1 Jun 2018

Keywords

  • Peakons
  • Serre equations
  • Solitary waves
  • Surface tension

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