Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear wave equation for a liquid with gas bubbles

Abstract

Liquids with gas bubbles are very common in science, engineering, physics, nature and life. Under investigation in this paper is a (3+1)-dimensional nonlinear wave equation for a liquid with gas bubbles. With respect to the velocity of the liquid-gas bubble mixture, we obtain the lump, rogue wave, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions via the symbolic computation. Based on the mixed lump-stripe soliton solutions, we construct the rogue wave and investigate the fusion and fission phenomena between a lump and the one-stripe soliton. We graphically study the mixed lump-stripe soliton under the influence of the parameters β, γ, δ and ξ, which represent the dispersion, perturbed effect, disturbed wave velocities along the y and z (i.e., the two transverse) directions, respectively. With the decreasing value of β to -1, the graph from a lump and one-stripe soliton shows a soliton; with the increasing value of γ to -3, location of the lump moves along the negative x axis; with the value of δ increasing to 0.5, location of the lump moves along the positive x axis; with the increasing value of ξ to -3, location and range of the lump soliton keep unchanged. With respect to the velocity of the mixture, we obtain the interaction between a rogue wave and a pair of stripe solitons according to mixed rogue wave-stripe soliton solutions. A lump is provided.