The Whitham equation with surface tension

@article{Dinvay2020TheWE,
  title={The Whitham equation with surface tension},
  author={Evgueni Dinvay and Daulet Moldabayev and D. Dutykh and H. Kalisch},
  journal={Nonlinear Dynamics},
  year={2020},
  volume={88},
  pages={1125-1138}
}
The viability of the Whitham equation as a nonlocal model for capillary-gravity waves at the surface of an inviscid incompressible fluid is under study. A nonlocal Hamiltonian system of model equations is derived using the Hamiltonian structure of the free-surface water-wave problem and the Dirichlet–Neumann operator. The system features gravitational and capillary effects, and when restricted to one-way propagation, the system reduces to the capillary Whitham equation. It is shown numerically… Expand
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  • 10
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References

SHOWING 1-10 OF 40 REFERENCES
Exact Evolution Equations for Surface Waves
  • 58
  • PDF
A numerical study of the Whitham equation as a model for steady surface water waves
  • 14
  • PDF
On the water-wave equations with surface tension
  • 130
  • PDF
Stability of traveling wave solutions to the Whitham equation
  • 40
  • PDF
Hamiltonian Long Wave Expansions for Free Surfaces and Interfaces
  • 189
  • PDF
Modulational Instability in the Whitham Equation with Surface Tension and Vorticity
  • 24
  • PDF
Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons
  • 4
  • Highly Influential
Stability of periodic waves of finite amplitude on the surface of a deep fluid
  • 1,976
  • PDF
A Numerical Study of the Exact Evolution Equations for Surface Waves in Water of Finite Depth
  • 56
  • PDF
...
1
2
3
4
...