Stability Theory of Flat Band Solitons in Nonlinear Wave Systems

Explore the stability theory of flat band solitons in nonlinear wave systems through this 51-minute lecture from the Simons Foundation. Delve into the dynamics of waves in crystalline media with flat or nearly flat spectral bands, which enable the existence of localized, non-transporting, and non-dispersing wavepackets that enhance interactions in condensed matter and nonlinear effects in photonics. Learn about the stability analysis of "minimal compact solitons" (MCS states) in the discrete nonlinear Schrödinger equation on multi-lattices supporting flat bands, with specific applications to diamond, Kagome, and checkerboard lattices. Discover how to engineer nonlinearity to stabilize small-amplitude MCS states in lattices where these states are naturally unstable, based on collaborative research with experts from Columbia University, University of Massachusetts Amherst, and IDA-CCRP.