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Cusp solitons mediated by a topological nonlinearity.

Harvey Cao1, Daniel Leykam2

  • 1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543.

Chaos (Woodbury, N.Y.)
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Summary

We introduce a new nonlinear Schrödinger model that uses wavefunction curvature to control nonlinear waves. This topological nonlinearity creates robust solitons and flat-top beams, offering new control methods for Bose-Einstein condensates and optics.

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Area of Science:

  • Nonlinear dynamics
  • Topological data analysis
  • Quantum physics

Background:

  • Nonlinearity in the Schrödinger equation drives phenomena like soliton formation and modulational instability.
  • Recent advances involve engineering nonlinear gauge fields in Bose-Einstein condensates and photonic lattices.

Purpose of the Study:

  • Introduce a novel nonlinear Schrödinger model incorporating wavefunction intensity curvature.
  • Investigate the link between this curvature-dependent dynamics and topological quantities.
  • Explore the potential for controlling nonlinear waves using topological nonlinearities.

Main Methods:

  • Developed a nonlinear Schrödinger model dependent on wavefunction intensity curvature.
  • Linked model dynamics to topological quantities from persistent homology.
  • Performed numerical simulations to observe emergent phenomena.

Main Results:

  • Demonstrated that topological nonlinearity energetically penalizes or favors local extrema.
  • Observed the emergence of robust, cusp-like soliton structures.
  • Showcased the support of flat-top beams immune to conventional modulational instability.

Conclusions:

  • Topological nonlinearities offer a new paradigm for controlling nonlinear waves.
  • The developed model provides a versatile tool for applications in Bose-Einstein condensates and optics.
  • This approach enables the creation of stable, engineered wave structures.