M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

Abstract

In this work, N-soliton waves, fusion solutions, mutiple M-lump solutions and the collision phenomena between one-M-lump and one-, two-soliton solutions to the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation are successfully revealed. A class of one-, two-, three-soliton, one-, two-fusion solutions are derived via the Hirota bilinear method and 1-M-lump, 2-M-lump solutions are constructed via the long-wave method. Moreover, physical collision phenomenon of 1-M-lump with one-, two-soliton solutions and also, with fusion solutions are successfully presented. The velocity of the 1-M-lump wave in x- and y-direction are also studied.