毛细引力Whitham方程的数值分歧与稳定性
Numerical bifurcation and stability for the capillary-gravity Whitham equation
摘要：
本文采用一种稳健的数值延拓方法研究了毛细-重力Whitham方程周期行波的全局分支，该方法结合了毛细-重力波线性理论中的频散和浅水非线性。我们采用了高度精确的数值方法进行空间离散和时间步进，以解决轨道稳定性和不稳定性的丰富多样的解决方案。我们的发现可以帮助分类毛细重力波和了解他们的长期动态。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
