From Laurent Series to Exact Meromorphic Solutions: the Kawahara equation

TL;DR

This paper derives nonlinear evolution equations for pressure waves in gas-liquid mixtures considering viscosity and heat transfer, and finds exact solutions to understand wave properties.

Contribution

It introduces new second and third order nonlinear evolution equations for gas-liquid mixtures and provides their exact solutions.

Findings

Exact solutions elucidate wave behavior in bubbly liquids.

Viscosity and heat transfer significantly affect wave propagation.

Properties of nonlinear waves are discussed in detail.

Abstract

Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order for describing nonlinear waves in gas-liquid mixtures are derived. Exact solutions of these nonlinear evolution equations are found. Properties of nonlinear waves in a liquid with gas bubbles are discussed.