Speaker: Dmitry Pelinovsky, McMaster University
Date: May 16, 2024
Title: On smooth and peaked traveling waves in a local model for shallow water waves
Abstract: I will describe a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for dynamics of shallow water waves. It allows us to characterize the traveling periodic waves both in the case of smooth and peaked waves and to solve the existence problem exactly, albeit not in elementary functions. Spectral stability of smooth waves with respect to co-periodic perturbations is proven analytically based on the exact count of eigenvalues in a constrained spectral problem.
Location: Residents of Lewis Hall can attend talks in the Wan Conference Room (Lewis 208) at 11:30am. The talk will also be streamed live via Zoom.