Abstract
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 language | English (US) |
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Article number | 102793 |
Journal | Wave Motion |
Volume | 106 |
DOIs | |
State | Published - Nov 2021 |
Keywords
- 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