Localized waves and interaction solutions to an integrable variable coefficients Jimbo-Miwa equation

In this paper, the reduced variable coefficients Jimbo-Miwa (vcJM) equation is studied. Firstly, the integrability of the reduced vcJM equation is verified by Painlevé analysis. Based on the Hirota bilinear method and the long wave limit method, the N-soliton solutions, rational and semirational solutions of the vcJM equation are obtained. By choosing different parameters and coefficient functions, some of different kinds of local waves, including of solition, breather wave and lumps, of the equation are obtained. Furthermore, the interaction solutions between different local waves are obtained. The dynamical behavior of the interaction between different local waves is studied by modifying the time parameters and the process is displayed by figures.