Asymptotic analysis and dynamics of nondegenerate bright–dark solitons in vector nonlinear Schrödinger equations

This study is devoted to the asymptotic analysis and dynamical exploration of multiple nondegenerate bright–dark (ND-BD) soliton solutions arising in three-component vector nonlinear Schrödinger equations with general nonlinear interaction coefficients. These solutions are formulated in explicit and concise determinant form using the bilinear method. We analyze the fundamental ND-BD soliton solutions and identify two types of soliton structures, namely the ( 1 , 1 , 1 ) - and ( 1 , 1 , 2 ) -solitons, characterized by whether the velocities of the nondegenerate bright soliton in two distinct components coincide or differ. The ( 1 , 1 , 1 ) -solitons exhibit a rich variety of profiles, including single-hump/valley, double-hump/valley, and flat-top/bottom structures, and may display symmetric or asymmetric shapes. The classification of these profiles is rigorously justified through the analysis of extrema and underlying symmetry. The ( 1 , 1 , 2 ) -solitons are restricted to single-hump/valley structures, and experience noticeable phase shifts as either the temporal or spatial variable approaches ± ∞ . The asymptotic analysis on multiple ND-BD (1,1,1)- and ( 1 , 1 , 2 ) -soliton solutions are performed to reveal detailed collision properties. Beyond the previously studied shape-preserving and shape-altering collisions involving all solitons, we uncover a new and previously unreported collision scenario where one soliton maintains its original profile while the other experiences a change in shape. The specific parametric conditions governing these shape-altering/preserving behaviors are explicitly provided. Our results enrich the understanding of vector ND-BD multi-soliton collision dynamics in nonlinear systems. • Explicit ND-BD solitons are derived for three-component vector NLS equations. • Symmetry and profile types are characterized by explicit analytical criteria. • Asymptotic analysis reveals rich collision dynamics in multi-soliton cases. • A novel collision scenario is uncovered, where one soliton preserves its shape while the other undergoes shape transformation.