Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

@article{Crosta2011BistabilityAI,
  title={Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schr{\"o}dinger equation},
  author={M. Crosta and Andrea Fratalocchi and Stefano Trillo},
  journal={Physical Review A},
  year={2011},
  volume={84},
  pages={063809}
}
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schroedinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock… 

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References

SHOWING 1-10 OF 24 REFERENCES

Phys

  • Rev. Lett. 77, 1193
  • 1996

Phys

  • Lett. A 128, 52
  • 1988

I and J

OPTICS COMMUNICATIONS

  • 1994

Phys

  • Scr. 39, 673
  • 1989

Phys

  • Rev. A 35, 466
  • 1987

Phys

  • Rev. E 64, 036617
  • 2001

Phys

  • Rev. Lett. 55, 1291
  • 1985

Nature Phys

  • 3, 46
  • 2007