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

TL;DR

This paper investigates complex interaction phenomena between lump and solitary waves in a generalized (3+1)-dimensional nonlinear wave equation relevant to liquids with gas bubbles, revealing various wave structures and behaviors.

Contribution

It introduces new interaction solutions between lump and solitary waves for a variable-coefficient nonlinear wave equation using Hirota's bilinear method.

Findings

Identified periodic-shape, parabolic-shape, and cubic-shape lump solutions.

Demonstrated interactions between lump and one or two solitary waves.

Analyzed bright lump and bright-dark lump wave structures.

Abstract

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