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
Original Article


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.


Serre equations Solitary waves Surface tension Peakons 

Mathematics Subject Classification

35Q35 74J30 92C35 


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M. A. Hoefer was partially supported by NSF CAREER DMS-1255422. D. Mitsotakis was supported by the Marsden Fund administered by the Royal Society of New Zealand. The authors would also like to thank the anonymous referees for their valuable comments and suggestions that helped to improve the original manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LAMA, UMR 5127 CNRSUniversité Savoie Mont BlancLe Bourget-du-Lac CedexFrance
  2. 2.Department of Applied MathematicsUniversity of ColoradoBoulderUSA
  3. 3.School of Mathematics and StatisticsVictoria University of WellingtonWellingtonNew Zealand

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