Dispersion

Dispersion introduces asynchronism in the nonlinear interaction of frequency components in a wave, which reduces the efficiency of energy transfer between harmonics. Two examples of weak dispersion are considered, one due to relaxation, for which an analytical solution for a step shock is available, and another due to thermoviscous boundary layers in ducts. Strong dispersion is considered for propagation of sound in nonplanar waveguide modes, with a nonlinear Schrödinger equation presented for narrowband pulses. Also considered is propagation in bubbly liquids, with a nonlinear evolution equation and coefficient of nonlinearity developed for sound at frequencies below the bubble resonances.