On soliton solutions, periodic wave solutions, asymptotic analysis and interaction phenomena of the (3+1)-dimensional JM equation

In this paper, the M-lump solutions, the periodic type, and cross-kink wave solutions are acquired. Here, the Hirota bilinear operator is employed. By utilizing the symbolic computation and employing the utilized method, the (3+1)-dimensional Jimbo–Miwa (JM) equation is investigated. Based on the Hirota bilinear form, the soliton solution and periodic wave solution to the mentioned equation, respectively, are obtained. We gained plenty of multiple collisions of lumps. Next, the periodic wave and cross-kink wave have greatly enriched the existing literature on the JM equation. Through the three-dimensional designs, contour design, density design, and two-dimensional design by using Maple, the physical features of these soliton solutions are explained all right. The forms of the attained solutions are one-lump, two-lumps, and three-lumps wave solutions. Then, a class of rogue waves-type solutions to the (3+1)-dimensional JM equation within the frame of the bilinear equation is found. These results can help us better understand interesting physical phenomena and mechanisms.