Vera Hur (UIUC)
Instabilities in nonlinear dispersive waves

I will speak on the wave breaking and the modulational instability of
nonlinear wave trains in dispersive media. I will begin by a gradient blowup
proof for the Boussinesq-Whitham equations for water waves. I will then
describe a variational approach to determine instability to long wavelength
perturbations for a general class of Hamiltonian systems, allowing for
nonlocal dispersion. I will discuss KdV type equations with fractional
dispersion in depth. Lastly, I will explain an asymptotics approach for
Whitham's equation for water waves, qualitatively reproducing the
Benjamin-Feir instability of Stokes waves.