Far-field analytical solutions of the non-homogeneous Helmholtz and wave equations for spatially non-localized sources.

Non-localized impulsive sources are ubiquitous in underwater acoustic applications. However, analytical expressions of their acoustic field are usually not available. In this work, far-field analytical solutions of the non-homogeneous scalar Helmholtz and wave equations are developed for a class of spatially extended impulsive sources. The derived expressions can serve as benchmarks to verify the accuracy of numerical solvers.