Green economy is a major them of sustainable development. The application of biological waste in engineering is conducive to green development. This study reveals the effect of recycled eggshell waste on the physical and chemical properties as well as nano-microstructure characteristics of asphalt. The hardness, thermal stability and ductility of asphalt were explored by the penetration, softening point and ductility tests. The distribution and relative content of protons in asphalt were revealed by nuclear magnetic resonance hydrogen spectrum (1H-NMR). The microscopic characteristics of the particle morphology and surface structure of the eggshell powder were explored by scanning electron microscopy (SEM). An atomic force microscope (AFM) was used to analyze the evolution laws of asphalt nano-microstructures. The experiment results indicate that (1) the eggshell waste increases the hardness, thermal stability and reduces the ductility of asphalt; (2) the chemical environment in which the protons of the eggshell waste asphalt are located and the H index have no obvious changes; (3) the eggshell powder is characterized by a rough, wrinkled, porous and loosened structure; (4) the nano-microstructure of eggshell waste asphalt exhibits “bee-like structures”, and the different proportion of eggshell waste changes the maturity, size and quantity of the “bee-like structures” and roughness, which can be attributed to the interaction of the asphaltene-waxiness system.

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In this paper, new solutions of the time-fractional Hirota–Satsuma coupled KdV equation model the intercommunication between two long waves that have well-defined dispersion connection received successfully by the unified method, the improved [Formula: see text]-expansion method and the homogeneous balance method. In contrast, these methods are simple and efficient, and can obtain different exact solutions to this equation. By symbolic calculation, polynomial solutions, hyperbolic function solutions, trigonometric function solutions, rational function solutions, etc. are acquired. Furthermore, we plot and analyze some solutions.

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Under investigation in this paper is the $(2+1)$ ( 2 + 1 ) -dimensional integrable coupling of the KdV equation which has applications in wave propagation on the surface of shallow water. Firstly, based on the Lie symmetry method, infinitesimal generators and an optimal system of the obtained symmetries are presented. At the same time, new analytical exact solutions are computed through the tanh method. In addition, based on Ibragimov’s approach, conservation laws are established. In the end, the objective figures of the solutions of the coupling of the KdV equation are performed.