Ben Zion Steinberg
Dept. of Interdisciplinary Studies, Faculty of Eng., Tel-Aviv Univ., Tel-Aviv 69978, Israel
A new wave equation that governs the evolution of local spectra of wave fields in a general nonhomogeneous environment is developed. The equation is obtained by applying the windowed Fourier transform directly to the Helmholtz wave equation. It is shown how simple analytical solutions of the new wave equation in a general smoothly varying nonhomogeneous environment can be obtained using well-known analytical techniques, and how the marching methodology connects these new solutions to the original problem described by the Helmholtz equation.