We investigate the deterministic generation of dark soliton trains in one-dimensional Bose–Einstein condensates based on a hybrid model combining a box-type density defect with step-phase imprinting. We solve the direct-scattering problem for a piecewise-constant initial wave function and, within the framework of the inverse-scattering transform, derive the discrete spectrum associated with the dark solitons. An explicit phase-sum conservation law is identified, linking the condensate's asymptotic phase difference to the individual soliton phase angles. Numerical simulations of the Gross–Pitaevskii equation confirm the theoretical predictions, demonstrating that the soliton trains obey the asymptotic superposition approximation. Extending the analysis to a harmonically trapped condensate, we show that, for a finite step-phase width $2L$, the soliton properties remain remarkably robust under weak confinement.

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• Cold atoms & matter waves
• Pattern formation
• Bose-Einstein condensates
• Nonlinear waves
• Solitons