arXiv subjects

Yuandi Xu

Publications and source records attributed to Yuandi Xu.

3 recordsLinked to original sources

arXiv2026

Matrix-free numerical continuation of the Ikeda map in passive Kerr resonators

We introduce a matrix-free numerical continuation framework for the Ikeda map of coherently driven passive Kerr resonators. The framework traces solution branches and evaluates their linear stability without explicitly assembling the full Jacobian matrices, using a unified formulation for states that recur after one or multiple round trips. We resolve stable and unstable branches of modulation-instability patterns and temporal cavity solitons, and uncover period-doubled homogeneous states and associated multi-round-trip dynamics that are absent from the standard Lugiato-Lefever equation (LLE). For period-1 states, the Ikeda map and the LLE show close agreement in the high-finesse regime, while their branch-existence intervals increasingly deviate as the finesse decreases. These results demonstrate that direct continuation of the unaveraged round-trip map can capture nonlinear states and multi-round-trip dynamics beyond the mean-field description, providing a systematic framework for bifurcation and stability analysis of Kerr resonators without relying on the averaged LLE.

physics.optics↗

arXiv2026

Residual-Certified Adaptive Tracking of Solution Manifolds in Parametric Dynamical Systems

This paper presents a residual-certified adaptive method for tracking local solution manifolds in parametric dynamical systems. The method combines local POD reduction, full physical residual checks, state-distance snapshot forgetting, high-fidelity resampling, and a lightweight physics-informed neural correction. Instead of learning one global parameter-to-state map, the algorithm maintains the currently active local branch and updates it when the residual indicates loss of validity. The analysis explains why residual thresholds are meaningful on regular branches through local residual-error control, and why stricter local updates are needed near folds or other degenerate neighborhoods. Numerical studies on Ostwald ripening, a particle population-balance model, and the Bratu equation test the approach across low-dimensional dynamics, nonlinear nonlocal residual compensation, and near-fold model failure. The results show that residual-certified local model management can concentrate high-fidelity computation in difficult parameter regions while preserving an interpretable link between surrogate prediction, physical consistency, and active-branch tracking.

math.NA↗

arXiv2026

Symmetry-Broken Cavity Solitons and Collective Polarization Conformity in Fabry-Perot Kerr Resonators

We report on the experimental generation of polarization symmetry-broken cavity solitons (CSs) in a passive, fiber-based, coherently-driven, Fabry-Perot (FP) Kerr resonator. Polarization resolved measurements reveal the spontaneous transition of initially symmetric CSs into asymmetrical vectorial states, triggered by a cross-phase modulation-induced polarization bifurcation. Most notably, due to counter-propagation of light occurring in FP resonators, we unveil a collective polarization conformity effect, whereby multiple CSs circulating in the cavity converge to the same asymmetric polarization state once their number exceeds a certain threshold. These results demonstrate that Fabry-Perot resonators support novel collective soliton dynamics that are absent in ring architectures.

physics.optics↗