ArticleScientific reports2026
Soliton management in a variable-coefficient coupled dispersionless system via Darboux transformation.
Article in Scientific reports, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
We study a coupled dispersionless system in [Formula: see text] dimensions with a time-dependent coefficient in the nonlinear coupling. The model consists of a real field u(x, t) and a complex field [Formula: see text], driven by a prescribed modulation function [Formula: see text]. A [Formula: see text] Lax pair of Zakharov-Shabat type is constructed, showing that the system remains integrable with the temporal dependence confined to diagonal terms of the Lax matrices. Using a Darboux transformation adapted to this Lax pair, we derive Wronskian-type formulas for multi-soliton solutions and obtain explicit families of bright and dark traveling waves for several representative choices of [Formula: see text]. In addition, a time reparametrization transforms the model to an autonomous form whose traveling-wave reduction yields a planar Hamiltonian system with equilibria and phase portraits identical to the constant-coefficient coupled dispersionless equations. The modulation [Formula: see text] therefore leaves the intrinsic traveling-wave dynamics unchanged but reshapes how these waves are embedded in the (x, t)-plane, enabling management of soliton amplitudes, velocities and curved or oscillatory trajectories.
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