Localization and shock waves in curved manifolds
The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by the nonlinear Schrödinger equation. At high bending and high nonlinearity, topological trapping is frustrated by the generation of curved wave-breaking. Four-dimensional parallel simulations confirm the theoretical model. This work may contribute to novel devices based on geometrically constrained highly nonlinear dynamics and tests and analogs of fundamental physical theories in curved space.
KeywordsNonlinear waves Shock waves Nonlinear optics Curvature Bose–Einstein condensation
This publication was made possible through the support of a grant from the John Templeton Foundation (58277). The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation. We also acknowledge support by the European Research Council Grant ERC-POC-2014 Vanguard (664782).
Conflict of interest
authors declare that they have no conflict of interest.
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