Proves the VK criterion applies to quasilinear GP dark solitons, implying stability for weak quasilinear terms and conditional stability (fast stable, slow unstable) for stronger terms due to an energy-momentum cusp.
StationarySolutionsoftheWaveEquationinaMedium with Nonlinearity Saturation.Radiophysics and Quantum Electronics, 16(7):783–789, July 1973
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Stability and instability of the quasilinear Gross--Pitaevskii dark solitons
Proves the VK criterion applies to quasilinear GP dark solitons, implying stability for weak quasilinear terms and conditional stability (fast stable, slow unstable) for stronger terms due to an energy-momentum cusp.