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In this paper, a generalized (3 + 1)-dimensional variable-coefficientnonlinear-wave equation is studied in liquid with gas bubbles. Based on theHirota's bilinear form and symbolic computation, lump and interaction solutionsbetween lump and solitary wave are obtained. Their interaction phenomena isshown in some 3d graphs and contour plots, which include a periodic-shape lumpsolution, a parabolic-shape lump solution, a cubic-shape lumpsolution,interaction solutions between lump and one solitary wave, and betweenlump and two solitary waves. The spatial structures called the bright lump waveand the bright-dark lump wave are discussed. Interaction behaviors of twobright-dark lump waves and a periodic-shape bright lump wave are alsopresented.

communications in theoretical physics/communications in theoretical physics

Interaction phenomena between lump and solitary wave of a generalized (3  + 1)-dimensional variable-coefficient nonlinear-wave equation in liquid with  gas bubbles