5 problems

Gaussian beam frequency-scale conjecture. The approach developed in the paper should remain applicable, after modifying the ansatz to account for these correcting terms, with the f…

Let $v(x,t;k)$ be a superposition of Gaussian beams with frequency parameter $k$, and let $u_{exact}(x,t)$ denote the exact solution. For the initial data described above, suppose…

Uniform stochastic regularity conjecture. The estimate holds, with constants $C_{\bold k}$ independent of the wavelength $\varepsilon$, for the stated Gaussian beam approximation a…

Even-order optimal-error conjecture. For beams of even order $k$, the theoretical result is sharp, giving an optimal energy-norm error estimate of

Odd-order convergence-gain conjecture. This gain of convergence is due to error cancellations and is present for all Gaussian beam superpositions with beams of odd order $k$.