Integrable models of transverse and longitudinal acoustic pulses evolution in a paramagnetic crystal with spin S=12 impurities

We study the interaction of transverse and longitudinal acoustic pulses propagating in a surface or crystal layer containing ion impurities with an effective spin S=12. We derive an evolution equations and show that coherent dynamics of acoustic pulses propagated under the condition of their unidirectional propagation is described by a new integrable system of evolution equations. The derived model describes the picosecond acoustic pulses dynamics corresponding to so called “a few cycle pulses”. To investigate an integrable reduction of the common model the inverse scattering transform is used. It is found that strong interaction of two components of the acoustic waves leads to formation of coupled soliton–antisoliton pairs.