Nonlinear evolution equations for describing waves in bubbly liquids with viscosity and heat transfer consideration

TL;DR

This paper derives and analyzes fourth-order nonlinear evolution equations for pressure waves in bubbly liquids, incorporating viscosity and heat transfer effects, and finds exact solutions to understand wave properties.

Contribution

It introduces a new fourth-order nonlinear evolution equation for bubbly liquids that includes viscosity and heat transfer, with exact solutions provided.

Findings

Exact solutions of the nonlinear evolution equation are obtained.

Viscosity and heat transfer significantly influence wave behavior.

Properties of nonlinear waves in bubbly liquids are discussed.

Abstract

Nonlinear evolution equations of the fourth order and its partial cases are derived for describing nonlinear pressure waves in a mixture liquid and gas bubbles. Influence of viscosity and heat transfer is taken into account. Exact solutions of nonlinear evolution equation of the fourth order are found by means of the simplest equation method. Properties of nonlinear waves in a liquid with gas bubbles are discussed.