# Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture

## TL;DR

This paper derives a new two-dimensional nonlinear PDE for gas-liquid mixture waves, investigates its integrability, constructs exact solutions, and performs numerical analysis to understand nonlinear wave behavior.

## Contribution

It introduces a novel extended 2D nonlinear equation for gas-liquid mixtures, including high-order terms, and analyzes its integrability and solutions.

## Key findings

- The derived equation is integrable under certain parameter conditions.
- Exact solutions of the equation are constructed.
- Numerical simulations reveal wave dynamics described by the equation.

## Abstract

We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the description of density perturbations of mixture in the two-dimensional case. We investigate integrability of this equation using the Painlev\'e approach. We show that travelling wave reduction of the equation is integrable under some conditions on parameters. Some exact solutions of the equation derived are constructed. We also perform numerical investigation of the nonlinear waves described by the derived equation.