Periodic Traveling Water Waves with Isobaric Streamlines

Periodic Traveling Water Waves with Isobaric Streamlines

It is shown that in water of finite depth, there are no periodic traveling waves with the property that the pressure in the underlying fluid flow is constant along streamlines. In the case of infinite depth, there is only one such solution, which is due to Gerstner.

Analyticity of periodic traveling free surface water waves with vorticity

We prove that the profile of a periodic traveling wave propagating at the surface of water above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the wave speed exceeds the horizontal fluid velocity throughout the flow. The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Hölder continuously differentiable.

Analyticity of the Streamlines for Periodic Travelling Free Surface Capillary-Gravity Water Waves with Vorticity

For capillary-gravity water waves with vorticity we prove that all streamlines beneath the surface are real analytic.

Periodic Traveling Waves in Diatomic Granular Chains

Periodic traveling waves in SIRS endemic models

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infectionwave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the tem...