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.
Angulo Pava.Nonlinear dispersive equations, volume 156 ofMathematical Surveys and Monographs
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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.