Numerical bifurcation and stability for the capillary-gravity Whitham equation
Fluid Dynamics
2021-08-27 v1 Dynamical Systems
Pattern Formation and Solitons
Abstract
We adopt a robust numerical continuation scheme to examine the global bifurcation of periodic traveling 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.
Cite
@article{arxiv.2102.01905,
title = {Numerical bifurcation and stability for the capillary-gravity Whitham equation},
author = {Efstathios G. Charalampidis and Vera Mikyoung Hur},
journal= {arXiv preprint arXiv:2102.01905},
year = {2021}
}
Comments
24 pages, 22 figures