Yifeng Mao, Department of Applied Mathematics, University of Colorado Boulder

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics

Waves and their interactions are ubiquitous in nature. While linear wave equations exhibit a superposition principle, nonlinear wave equations generally do not.

A complicated class of problems, including periodic traveling waves and their interactions across multiple phases, presents a rich and physically meaningful area. Inspired by this, the primary objective of this work is the mathematical and experimental study of nonlinear wave interactions, starting from the generation and propagation of one-phase periodic traveling waves and extending to their two-phase interactions with solitons and with one another.

The talk focuses on multiscale nonlinear wave phenomena within a dispersive hydrodynamic framework in which waves in fluid and fluid-like systems are subject to dispersion that dominates dissipation. The research combines analytical and asymptotic techniques, numerical simulations in two specific models: the Korteweg–De Vries (KdV) equation and the conduit equation, and experimental observations in a viscous core-annular flow system.