Weakly nonlocal gravity-capillary solitary waves

T. S. Yang, T. R. Akylas

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


There is evidence from previous analytical work based on a model equation and from numerical computations that gravity-capillary solitary waves in a liquid layer are nonlocal - they feature oscillatory tails of constant amplitude - when the Bond number τ is less than 1/3. Here, the full gravity-capillary wave problem is examined and these tails are calculated asymptotically in the weakly nonlinear regime. For given values of τ(0<τ<1/3) and Froude number F slightly greater than 1, there exists a one-parameter family of weakly nonlocal solitary waves characterized by the phase shift of the tails relative to the main peak. The tail amplitude depends on the phase shift and is exponentially small with respect to the wave peak amplitude. Predictions of the asymptotic theory are confirmed by numerical computations using a spectral method,

Original languageEnglish
Pages (from-to)1506-1514
Number of pages9
JournalPhysics of Fluids
Issue number6
Publication statusPublished - 1996 Jun

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes
  • Computational Mechanics


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