Monday, October 22, 2018 | 3:30 PM | PHSC 1105 |

The Ostrovskyi (Ostrovskyi-Vakhnenko/short pulse) equations are ubiquitous models in mathematical physics. They describe water waves under the action of a Coriolis force as well as the amplitude of a "short" pulse in an optical fiber.

I will talk about constructing ground traveling waves for these models as minimizers of the Hamiltonian among all waves with fixed *L*^{2} norm. The existence argument proceeds via the method of compensated compactness, but it requires surprisingly detailed Fourier analysis arguments to rule out the non-triviality of the limits of the minimizing sequences. We show that (at least almost all of) the waves are strongly spectrally stable, along with other properties: smoothness with respect to parameters, weak non-degeneracy of the waves etc.

In the case of quadratic nonlinearities, it is known that these waves are unique, by work of Zhang-Liu. Thus, our results imply in particular that (at least almost all of) the Zhang-Liu waves are spectrally stable. This is joint work with professor A. Stefanov.