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

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 travelling wave solutions are presented in the case of critical surface tension. The numerical experiments were performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order four.

Keywords

Bibliographic record

BibTeX Citation

@article{Dutykh2018solitarywave,
  author = {Dutykh, D. and Hoefer, M. and Mitsotakis, D.},
  title = {Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations},
  journal = {Theor. Comp. Fluid Dyn.},
  year = {2018},
  volume = {32},
  number = {3},
  pages = {371--397},
  doi = {10.1007/s00162-018-0455-3},
  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 travelling wave solutions are presented in the case of critical surface tension. The numerical experiments were performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge-Kutta method of order four.},
  keywords = {Serre equations, surface tension, solitary waves, peakons}
}