Dark Solitons, Dispersive Shock Waves, and Transverse Instabilities

@article{Hoefer2012DarkSD,
  title={Dark Solitons, Dispersive Shock Waves, and Transverse Instabilities},
  author={Mark A. Hoefer and Boaz Ilan},
  journal={Multiscale Model. Simul.},
  year={2012},
  volume={10},
  pages={306-341}
}
The nature of transverse instabilities of dark solitons for the (2+1)-dimensional defocusing nonlinear Schrodinger/Gross–Pitaevskii˘ (NLS/GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev–Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS/GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields (1) the… 

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