Observations and applications of nonlinear acoustic phenomena in superfluid3He-B are reported. Two-phonon absorption (TPA) by the real squashing (rsq) mode has been detected under several experimental conditions below p = 3.5 bar, using two coincident sound pulses. The attenuation peak height has been investigated as a function of the energy densities of the two sound waves. We discovered the five-fold Zeeman splitting of TPA by parallel sound pulses in an applied magnetic field and the two-fold dispersion splitting due to the finite wave vector of the mode when the two sound pulses are mutually perpendicular. The dispersion relation of the real squashing mode has been investigated at zero pressure and in zero magnetic field by exciting the mode with two parallel, perpendicular, or antiparallel sound waves. Experimental values for the parameters that determine the collective-mode velocities have been extracted from the positions of the observed attenuation maxima. An anomalous structure has been observed in the attenuation and phase velocity spectra of a single high-intensity sound wave near the threshold for pair breaking by two phonons; in an applied magnetic field the phase velocity anomaly splits into a triplet.