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The multi-dimensional six-wave interaction system is derived in the context of nonlinear optics. Starting from Maxwell’s equations, a reduced system of equations governing the dynamics of the electric and polarization fields are obtained. Using a space–time multi-scale asymptotic expansion, a hierarchy of coupled equations describing the spatio-temporal evolution of the perturbed electric and polarization fields are derived. The leading order equation admits a six-wave ansatz satisfying a triad resonance condition. By removing secular terms at next order, a first order in space and time quadratically nonlinear coupled six-wave interaction system is obtained. This resulting system is tied to its integrable counterpart which was postulated by Ablowitz and Haberman in the 1970s. A reduction to a space–time shifted nonlocal three-wave system is presented. The resulting system is solved using the inverse scattering transform, which employs nonlocal symmetries between the associated eigenfunctions and scattering data; soliton solutions are then obtained. Finally, an infinite set of conservation laws for the six-wave system is derived; one is shown to be connected to its Hamiltonian structure. 

Abstract Supersaturated solid solutions of Al and corrosion-resistant alloying elements (M: V, Mo, Cr, Ti, Nb), produced by non-equilibrium processing techniques, have been reported to exhibit high corrosion resistance and strength. The corrosion mechanism for such improved corrosion performance has not been well understood. We present a fundamental understanding of the role of V in corrosion of an Al-V alloy, which will provide a theoretical background for developing corrosion-resistant Al alloys. High-energy ball milling of the elemental powder of Al and V produced an in situ consolidated Al-V alloy, which exhibited high solid solubility of V. The corrosion resistance of Al-V alloy was significantly higher than that of pure Al, which was attributed to the (1) enrichment of V at the passive film/substrate interface, (2) incorporation of V into the passive film, and (3) deposition of V on the iron-containing cathodic particles and therefore, retardation of cathodic reaction. 

Abstract Quantum Chromodynamics predicts a phase transition from hadronic matter to quark–gluon plasma (QGP) at high temperatures and energy densities, where quarks and gluons (partons) are no longer confined within hadrons. The QGP forms in ultrarelativistic heavy-ion collisions. Anisotropic flow coefficients, quantifying the azimuthal expansion of produced matter, probe QGP properties. Flow measurements in high-energy heavy-ion collisions show a distinctive grouping of anisotropic flow for baryons and mesons at intermediate transverse momentum – a feature associated with flow imparted at the quark level, confirming QGP existence. The observation of QGP-like features in proton–proton and proton–ion collisions has sparked debate about QGP formation in smaller systems. For the first time, we demonstrate the distinctive grouping of anisotropic flow for baryons and mesons in high-multiplicity proton–lead and proton–proton collisions at the Large Hadron Collider (LHC). These results are described by a model including hydrodynamic flow followed by hadron formation via quark coalescence, consistent with the formation of partonic flowing systems in these collisions.