Extended models of nonlinear waves in liquid with gas bubbles

Abstract

In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.

References in corpus (2)

• On asymptotically equivalent shallow water wave equations
• Evolution equation for bidirectional surface waves in a convecting fluid

Cited by in corpus (4)

• Special solutions of high order equation for waves in liquid with gas bubbles
• Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture
• Periodic structures described by the perturbed Burgers-Korteweg-de Vries equation
• Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: Further development of methodology with two applications