A transmutation approach to underwater sound propagation (Q580108)

A hybrid approach is used to combine analytical computations that model the major features of the ocean with symbolic and numerical computations that model the secondary features. Integral operators are used to transmute solutions of the Helmholtz equation with constant coefficients into solutions of the Helmholtz equation with variable coefficients. The kernels of these operators satisfy certain hyperbolic partial differential equations and characteristic conditions. The transmutations preserve some, but not all, of the boundary conditions given for the Helmholtz equation.