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

  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},
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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  • Rev. Lett. 77, 1193
  • 1996
Catastrophe Theory for Scientists and Engineers
I and J
  • 1994
  • Rev. A 74, 023623
  • 2006
  • Rev. A 82, 063829
  • 2010
  • Scr. 39, 673
  • 1989
  • Lett. A 128, 52
  • 1988
  • Am. B 28, 1583
  • 2011