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

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.

References in corpus (4)

• Meromorphic solutions of nonlinear ordinary differential equations
• Nonlinear waves in bubbly liquids with consideration for viscosity and heat transfer
• From Laurent Series to Exact Meromorphic Solutions: the Kawahara equation
• Explicit expressions for meromorphic solution of autonomous nonlinear ordinary differential equations

Cited by in corpus (4)

• Extended models of nonlinear waves in liquid with gas bubbles
• Extended equation for description of nonlinear waves in liquid with gas bubbles
• Interaction phenomena between lump and solitary wave of a generalized (3 + 1)-dimensional variable-coefficient nonlinear-wave equation in liquid with gas bubbles
• Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture