The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities
KAUST DepartmentPRIMALIGHT Research Group
Electrical Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractBy employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.
CitationThe Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities 2012, 14 (9):093019 New Journal of Physics
JournalNew Journal of Physics