On existence of dark solitons in cubic-quintic nonlinear Schr\"{o}dinger equation with a periodic potential
classification
🌊 nlin.PS
cond-mat.othernlin.CD
keywords
darkcubic-quinticdingerequationexistencenonlinearperiodicpotential
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A proof of existence of stationary dark soliton solutions of the cubic-quintic nonlinear Schr\"{o}dinger equation with a periodic potential is given. It is based on the interpretation of the dark soliton as a heteroclinic on the Poincar\'e map.
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