The synergistic regulation mechanism of nonreciprocal coupling and fractional diffraction on vector soliton collision dynamics remains unclear. In this paper, a spatial fractional-order cubic-quintic coupled nonlinear Schrödinger equation model is constructed, and the Strang splitting Fourier spectral method is employed to systematically investigate the synergistic effects of nonreciprocal coupling strength and fractional order on vector soliton collision behavior, revealing the scale-matching mechanism governing resonant radiation and its universal characteristics.
Methodologically, we unify the nonlocal dispersive properties of the fractional Laplacian operator with cubic-quintic nonlinear self-interaction and asymmetric cross-phase modulation coupling, establishing a general theoretical framework for describing vector soliton interactions in long-range correlated media. Numerical integration adopts the Strang operator splitting scheme, symmetrically coupling linear fractional dispersion evolution with nonlinear interaction, ensuring second-order symplectic accuracy and long-propagation stability. To address the Lévy super-diffusion instability in the low fractional-order regime (α ≤ 1.3), a piecewise adaptive initialization strategy is proposed, adjusting initial separation, evolution window, and incident velocity to guarantee comparability of collision events across different parameters.
In the reciprocal coupling limit, the system exhibits typical elastic scattering characteristics with a relative Hamiltonian error as low as 6.2×10-3 and zero momentum drift, indicating excellent conservation properties; under nonreciprocal coupling, velocity asymmetry increases monotonically with coupling imbalance |△γ|, while the Hamiltonian error remains stable in the weak nonreciprocal regime. Regarding fractional-order tuning: the classical limit (α = 2.0) shows minimal radiation loss (5.0×10^-4) and near-elastic scattering; the intermediate fractional-order region (α ≈ 1.43 - 1.48) exhibits weak resonant radiation with a peak loss of 0.0289 and center-of-mass drift of 6.67; the low fractional-order region (α ≤ 1.2) presents a super-focusing effect, with peak density sharply increasing from 4.49 at the classical limit to 47.88—more than one order of magnitude enhancement. Universal verification through two-dimensional parameter scanning reveals that the resonant position is strictly independent of incident velocity (△α_res = 0.06) but systematically dependent on soliton amplitude (△α_res = 0.5 for N ∈ 3.0, 7.0), confirming that the effect is jointly determined by the intrinsic scaling law of fractional-order transport and soliton eigenwidth.
Based on scale-matching mechanism analysis, optimal control windows are proposed—weak nonreciprocity (△γ < 0.2) for stable elastic collision, α ≥ 1.8 for low-loss transmission, and α ≤ 1.2 for enhanced local field intensity. This work, for the first time, unifies nonreciprocal coupling, fractional diffraction, and high-order nonlinearity in the study of vector soliton collision dynamics, revealing the synergistic competition between asymmetric momentum transfer and resonant radiation, providing theoretical guidance for the manipulation and application of coherent structures in nonreciprocal photonics and quantum transport.