Infinite-layer nickelates exhibit an anomalously weak superfluid response whose origin cannot be captured by a single stiffness scale. We test a two-scale interpretation in which a disorder-controlled dirty-d-wave condensate provides an intrinsic baseline for superconductivity, while phase-coherence effects account for departures from one-scale behavior. The endpoint relation between transition temperature and zero-temperature stiffness is approximately consistent with the global experimental trend, and the two-scale construction is consistent with the local crossover between the two observed regimes. The same framework explains why finite-temperature stiffness, anisotropic phase response and multiband electrodynamics may depart from a unique carrier-density scaling. It also yields a conditional irradiation test based on the joint evolution of transition temperature and superfluid stiffness. These results support a phenomenological two-scale picture in which disorder-sensitive pair breaking and phase coherence are both experimentally relevant, without uniquely assigning the limiting mechanism in every local region.
This paper investigates the integrability properties and exact solutions of a generalized Benjamin-Ono (BO) equation. The generalized BO equation is first transformed into coupled Burgers equations, and Painlevé analysis is performed to verify its weak Painlevé integrability. Lax pair representation is explicitly constructed to confirm its complete integrability. Furthermore, the connection between the generalized BO equation and the linear equation is established by means of the appropriate transformation. Based on the pole expansion method, the correspondence between the generalized BO equation and Calogero-Moser type dynamical system is revealed and a set of exact solutions is constructed.
