Large-amplitude modulation of periodic traveling waves

Second-order Perturbation Analysis of Low-amplitude Traveling Waves in a Periodic Nonlinear Chain

Traveling waves in one-dimensional nonlinear periodic structures are investigated for low-amplitude oscillations using perturbation analysis. We use second-order multiple scales analysis to capture the effect of quadratic nonlinearity. Comparisons with the linear and cubical nonlinear cases are presented in the dispersion relationship, group velocity and phase velocity and their dependence on w...

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.

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...

A Penalization Method for Calculating the Flow Beneath Traveling Water Waves of Large Amplitude

We suggest an algorithm for the calculation of large-amplitude traveling water waves in irrotational flows and in flows with constant and nonconstant vorticity, respectively. The algorithm is based on a quite general partial differential equation constrained optimization formulation, maximizing the wave amplitude subject to the PDE constraint that the Euler equations hold. Numerical examples il...