A (2+1)-dimensional nonlinear partial differential evolution (NLPDE) equation is presented as a model equation for relaxing high-rate processes in active barothropic media. With the aid of symbolic computation and Hirota's method, some typical solitary wave solutions to this (2+1)-dimensional NLPDE equation are unearthed. As a result, depending on the dissipative parameter, single and multivalued solutions are depicted.