arXane › Physics › Nonlinear Sciences
Wednesday, 4 November 2026: 1 new paper, 1 cross-list and 2 replacements in Pattern Formation and Solitons (nlin.PS), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
We investigate the interaction of dissipative Kerr solitons in two nearly identical coherently driven, coupled microresonators in the presence of third-order dispersion (TOD). Using an asymptotic reduction of the coupled Lugiato--Lefever equations, we derive effective interaction equations governing the soliton separation and collective drift for weak intercavity coupling. TOD breaks the parity symmetry of the soliton profile and qualitatively modifies the effective interaction, leading to asymmetric interaction forces and multiple stable and unstable soliton clusters. The existence and stability of these clusters are controlled by the relative phase of the driving fields and the group-velocity mismatch between the resonators. In particular, an appropriate value of the group-velocity mismatch can give rise to multiple stable bound states, whereas deviations from this value trigger successive saddle-node bifurcations, ultimately leading to periodic soliton collisions. The analytical predictions are confirmed by numerical simulations of the full coupled system.
Topological insulators can host chiral, disorder-robust edge states that dissipate energy when coupled to an external bath. We show that nonlinear interactions enable all-optical control over edge-state dissipation in a laser-written Floquet topological insulator periodically coupled to a photonic bath. Although moderate nonlinearity enhances dissipation due to mode mixing, increasing the nonlinear strength to an optimal value dramatically suppresses dissipation by forming highly localized traveling edge solitons. These results establish engineered system-bath coupling and nonlinear interactions as a route to suppress dissipation of chiral topological edge transport.