Some new solitary solutions of (3+1)-dimensional Jimbo-Miwa equation such as breather solutions, double breather solutions and mixed solutions of different forms are studied via applying Hirota's bilinear form and constructing various trial functions. Besides, the degradation phenomenon of breather solution to lump-type solution is investigated, and dynamical behaviours of the interaction between solitary solutions and lump-type solutions varying with time t is discussed. Finally, the interactive result between N-soliton solution (N takes any positive integer) and lump-type solution is studied by reducing dimension, and the detailed proof process is presented.

During deep-sea mining, heavy metal pollutants can cause contamination in the marine environment. In this paper, the multiphasic coupling model is established to describe the heavy metal migration process during deep-sea mining, which takes the effects of the convection–diffusion, adsorption–desorption, and sedimentation–resuspension of heavy metals in the aquatic environment into full consideration. Due to the advantages of the Lattice Boltzmann method, it is adopted to numerically solve the multiphasic coupling model and achieve the simulation of the heavy metal migration process during deep-sea mining. In addition, taking cadmium as an example, the concentration variations are discussed and analyzed in detail. Based on the established model and Lattice Boltzmann method, the concentration distribution of heavy metals can be accurately described to provide the reasonable bases for the evaluation of marine environmental protection.

During deep-sea mining, the heavy metals pollutants can cause contamination in the marine environment. In this paper, the multiphasic coupling model is established to describe the heavy metal migration process during deep-sea mining, which takes the effects of convection-diffusion, adsorption-desorption and sedimentation-resuspension of heavy metals in the aquatic environment into full consideration. Due to the advantages of Lattice Boltzmann method, it is adopted to numerically solve the multiphasic coupling model and achieve the simulation for heavy metal migration process during deep-sea mining. In addition, taking Cadmium as an example, the concentration variations are discussed and analyzed in detail. Based on the established model and Lattice Boltzmann method, the concentration distribution of heavy metals can be accurately described to provide the reasonable bases for the evaluation of marine environmental protection.