Localization of resonant spherical waves

This paper treats radial spherical resonant waves excited in the transresonant regime. An approximate general solution of a perturbed-wave equation is presented here, which takes into account nonlinear, spatial, and dissipative effects. Then the boundary problem reduces to the perturbed compound Burgers-Korteweg-de Vries equation (BKdV) in time. Several solutions to this equation are constructed. Shock waves may be excited near resonance according to the solutions for an inviscid medium. However, both viscosity and spatial dispersion begin to be important very close to resonance and prevent the formation of shock discontinuity. As a result, periodic localized excitations are generated in resonators instead of shock waves. © 2002 Plenum Publishing Corporation.