Numerical bifurcation and stability for the capillary–gravity Whitham equation

Efstathios G. Charalampidis, Vera Mikyoung Hur

Research output: Contribution to journalArticlepeer-review


We adopt a robust numerical continuation scheme to examine the global bifurcation of periodic travelling waves of the capillary–gravity Whitham equation, which combines the dispersion in the linear theory of capillary–gravity waves and a shallow water nonlinearity. We employ a highly accurate numerical method for space discretization and time stepping, to address orbital stability and instability for a rich variety of the solutions. Our findings can help classify capillary–gravity waves and understand their long-term dynamics.

Original languageEnglish (US)
Article number102793
JournalWave Motion
StatePublished - Nov 2021


  • Capillary-gravity Whitham equation
  • Global bifurcation
  • Orbital stability
  • Periodic travelling waves

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Physics and Astronomy
  • Computational Mathematics
  • Applied Mathematics


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