Science Bulletin

, Volume 61, Issue 7, pp 570–575 | Cite as

Localization and shock waves in curved manifolds

  • Claudio Conti
Article Physics & Astronomy


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.


Nonlinear 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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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute for Complex SystemsNational Research Council (ISC-CNR)RomeItaly
  2. 2.Department of PhysicsUniversity SapienzaRomeItaly

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