We show that the wave map equation in ${\bf R}^{1+1}$ is in general ill posed in the critical space $\dot{H}^{1/2}$, and the Besov space $\dot{B}_{2}^{1/2,1}$. The ...

We study wave propagation in a one-dimensional random medium whose index of refraction is characterized randomly and is assumed to have small fluctuations about the mean. The appropriate stochastic ...

BUFFALO, N.Y. — Last year, onlookers observed a startling site on China’s Qiantang River: waves forming a grid-like pattern. Dubbed the “matrix tide,” this complex wave pattern was caused by the river ...