Three wave solution and lump-type solution to a (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa equation with some variable coefficients in inhomogeneous media

This paper focuses on the new (3+1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation with some variable coefficients and derives its new analytical solutions. Based on the (2+1)-dimensional DJKM equation, this equation adds an additional spatial dimension (z) and introduces time-dependent coefficients. Therefore, it is more suitable for describing dynamic wave behaviors in inhomogeneous media. Firstly, by virtue of the Hirota method, we derive the Hirota bilinear form of the equation. Secondly, based on the bilinear form, we present three types of solutions, including the three wave solution and lump-type solution. Finally, by choosing appropriate parameters, we plot some graphs to intuitively display the physical characteristics of these solutions.