Science Bulletin

, Volume 61, Issue 7, pp 570–575

Localization and shock waves in curved manifolds

Article Physics & Astronomy

DOI: 10.1007/s11434-016-1040-z

Cite this article as:
Conti, C. Sci. Bull. (2016) 61: 570. doi:10.1007/s11434-016-1040-z


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 

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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