Lump-type and interaction solutions to an extended (3 + 1)-dimensional Jimbo–Miwa equation

Abstract

By using the Hirota bilinear method, we construct new lump-type solutions to an extended [Formula: see text]-dimensional Jimbo–Miwa equation, which describes certain [Formula: see text]-dimensional wave phenomena in physics. The presented solutions contain 10 arbitrary parameters and only need to satisfy four restrictive conditions to be analytic, thereby enriching the existing lump-type solutions. Moreover, we compute their interaction solutions with double exponential function waves, which include rogue wave solutions. Dynamical features of the obtained solutions are graphically exhibited.

Study of lump solutions to an extended Calogero-Bogoyavlenskii-Schiff equation involving three fourth-order terms

“…However, it is well known that interaction solutions between lump solutions and soliton solutions can describe more nonlinear phenomena [17,18] and various studies have shown the existence of interaction solutions between lumps and other kinds of exact solutions to nonlinear integrable equation [19][20][21][22][23][24], even in (3+1) dimension [25][26][27] and linear wave equation [28]. Since the interaction properties involve much more complicated mathematical computations, further investigation on related issues is needed.…”