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The dark soliton solution to Eq. (54, 55, 56) displays a localized intensity dip on a continuous wave background, as depicted in 3D and contour plots with suitable free parameters: \(\varrho =.98,~ a_1=0.85,~k_0=0.05,~\mu =-0.75,~\tau =0.7,~\text{ and }~\omega =0.55.\).
