The Nineteenth Israeli Mini-Workshop in Applied and Computational Mathematics

Boaz Ilan (University of California, Merced)

Nonlinear waves in inhomogeneous media

Nonlinear Schrödinger (NLS) equation models nonlinear wave propagation in water waves, optics, ultra-cold matter waves, and other physical systems. The NLS equation admits localized ground states solutions known as solitary waves or solitons, which play an important role in applications. These waves can be better confined and controlled when the ambient medium is inhomogeneous, such as in photonic crystal fibers. In this talk I will review some results of existence and stability of ground states in such equations with periodic and parity-time symmetric potentials.

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