Nonlinear system of PT-symmetric excitations and Toda vibrations integrable by the Darboux–Bäcklund dressing method

The nonlinear dynamics of coupled P T -symmetric excitations and Toda-like vibrations on a one-dimensional lattice are studied analytically and elucidated graphically. The nonlinear exciton-phonon system as the whole is shown to be integrable in the Lax sense inasmuch as it admits the zero-curvature representation supported by the auxiliary linear problem of third order. Inspired by this fact, we have developed in detail the Darboux–Bäcklund integration technique appropriate to generate a higher-rank crop solution by dressing a lower-rank (supposedly known) seed solution. In the framework of this approach, we have found a rather non-trivial four-component analytical solution exhibiting the crossover between the monopole and dipole regimes in the spatial distribution of intra-site excitations. This effect is inseparable from the pronounced mutual influence between the interacting subsystems in the form of specific nonlinear superposition of two essentially distinct types of travelling waves. We have established the criterion of monopole-dipole transition based upon the interplay between the localization parameter of Toda mode and the inter-subsystem coupling parameter.

Integrable variable-coefficient derivative Spin-1 Gross–Pitaevskii equations and their explicit solutions

Based on the generalized dressing method, we propose a new integrable variable coefficient Spin-1 Gross–Pitaevskii equations and derive their Lax pair. Using separation of variables, we have derived explicit solutions of the equations. In order to analyze the characteristic of derived solution, the graphical wave of the solutions is plotted with the aid of Matlab.

A Real-Time Dressing Method for Metal Lapping Pads Based on the Thermal-Deformation Effect

The surface shape and accuracy of the metal lapping pad are important factors that affect the performance of the lapping process for flat optical components. A real-time control system for metal-lapping-pad surface shape (RCLPS) based on the bimetal thermal-deformation effect is proposed. Unlike traditional dressing methods (e.g., turning dressing with a diamond tool), real-time dressing based on the RCLPS system is a material-loss-free and in-process dressing method. A full-aperture lapping turntable based on the RCLPS system was designed, and the working heat was analyzed. A thermal-deformation model was established through regression analysis. Finally, experiments were conducted to verify the functionality of the RCLPS system. During turning dressing (turntable rotational speed nm = 100 rpm), the thermal-deformation error caused by the working heat of the turntable-shaft system was compensated by the RCLPS system. During the lapping process for optical elements (nm ≤ 20 rpm), the real-time dressing of the lapping-pad surface shape was controlled by the coolant temperature of the RCLPS system, permitting optimization and adjustment of the process performance of the plane optical component. The effectiveness and practicality of the RCLPS system were demonstrated experimentally.