Equation for the three-dimensional nonlinear waves in liquid with gas bubbles

Nonlinear waves in a liquid containing gas bubbles are considered in the three-dimensional (3D) case. The nonlinear evolution equation is given for a description of long nonlinear pressure waves. It is shown that in the general case the equation is not integrable. Some exact solutions for the nonlinear evolution equation are presented. The application of the Hirota method is illustrated for finding multi-soliton solutions for the nonintegrable evolution equation in the 3D case. The stability of the 1D solitary waves is investigated. It is shown that the 1D solitary waves are stable to transverse perturbations.