On the steady solitary-wave solution of the Green-Naghdi equations of different levels

Bin Zhao, R. Cengiz Ertekin, W. Y. Duan, M. Hayatdavoodi

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21 Citations (Scopus)


The steady-state solitary wave solution of high-level Green-Naghdi (GN) equations is obtained by use of the Newton-Raphson method. Four aspects of solitary waves are studied: the wave speed, wave profile, velocity field and particle trajectory. A convergence study is performed for each individual case. Results of the converged model are compared with the existing laboratory experiments and other theoretical solutions for an inviscid and incompressible fluid, including the solutions of the Euler equations. Particle trajectories, predicted by the GN model, show close agreement with the laboratory measurements and provide a new approach to understanding the movement of the particles under a solitary wave. It is further shown that high-level GN equations can predict the solitary wave of the highest height.

Original languageEnglish
Pages (from-to)1382-1395
Number of pages14
JournalWave Motion
Issue number8
Early online date4 Sep 2014
Publication statusPublished - Dec 2014



  • High-level Green-Naghdi equations
  • Particle trajectories
  • Solitary wave
  • Steady solution

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