Exactly solvable wave dynamic models for liquids containing gas bubbles are presented. Lighthill’s generalized inhomogeneous wave equation is first derived for a host liquid where the gas phase is presented by an equivalent distribution of monopole sources. The complete effects of nonlinear bubble dynamics and the change of bubble number density in a pressure field are included. An exact numerical method, where individual bubbles are traced to estimate their radial dynamics and the full volumetric change of the wave phenomena, is developed and programmed for solution on a computer. ©2000 American Institute of Physics.