Ultrasonic dissipative soliton in a nonequilibrium paramagnetic crystal

The propagation of an ultrasonic gigahertz pulse in a low-temperature crystal containing paramagnetic ions with the inversed population of Zeeman sublevels of the resonance spin–phonon transition has been studied. An integrodifferential parabolic equation with a nonlinear autonomous source and irreversible losses has been obtained in the fast phase relaxation approximation for a local relative deformation of a pulse. The exact analytical solution of this equation in the form of a dissipative soliton with an asymmetric temporal profile has been obtained and analyzed in detail. The velocity of the soliton is close to the linear group velocity of ultrasound. It has shown that such a soliton can be formed only if irreversible losses caused by processes that are not related to spin–phonon transitions exist in addition to losses caused by the phase relaxation of spin–phonon transitions.