  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.
