有质量或无质量的周期性行进界面水弹性波 II：多重分岔与波纹
Periodic traveling interfacial hydroelastic waves with or without mass II: Multiple bifurcations and ripples
AI总结：
本文研究无限深度界面水弹性行进波中线性化核为二维的共振与非共振情形，利用隐函数定理证明波的存在性，并进行数值计算。
摘要：
在先前的工作中，作者证明了无限深度上空间周期性界面水弹性行进波的全局分岔定理，并计算了此类行进波。该行进波问题的解析与数值表述允许波高为多值函数。全局分岔定理要求相关映射线性化中的核为一维，但对于某些参数值，核变为二维。在本工作中，我们研究这些具有二维核的情形，它们出现在共振与非共振两种变体中。我们应用隐函数定理论证证明了在这两种情况下行进波的存在性。我们还在共振与非共振两种情况下对波进行了数值计算。
英文摘要：
In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling wave problem used both analytically and numerically allows for waves with multi-valued height. The global bifurcation theorem required a one-dimensional kernel in the linearization of the relevant mapping, but for some parameter values, the kernel is instead two-dimensional. In the present work, we study these cases with two-dimensional kernels, which occur in resonant and non-resonant variants. We apply an implicit function theorem argument to prove existence of traveling waves in both of these situations. We compute the waves numerically as well, in both the resonant and non-resonant cases.
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