Equation for three-dimensional nonlinear waves in liquid with gas bubbles

TL;DR

This paper derives a three-dimensional nonlinear wave equation for a liquid with gas bubbles, explores its solutions including multi-solitons, and investigates the stability of solitary waves, highlighting the equation's nonintegrability.

Contribution

It introduces a new three-dimensional nonlinear evolution equation for bubbly liquids and applies the Hirota method to find multi-soliton solutions, analyzing their stability.

Findings

The nonlinear evolution equation is generally nonintegrable.

Exact solutions, including multi-solitons, are obtained.

One-dimensional solitary waves are stable to transverse perturbations.

Abstract

Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional case. Nonlinear evolution equation is given for description of long nonlinear pressure waves. It is shown that in the general case the equation is not integrable. Some exact solutions for the nonlinear evolution equation are presented. Application of the Hirota method is illustrated for finding multi-soliton solutions for the nonintegrable evolution equation in the three-dimensional case. The stability of the one-dimensional solitary waves is investigated. It is shown that the one-dimensional solitary waves are stable to transverse perturbations.