Resonance vector soliton of the Rayleigh wave

A theory of acoustic vector solitons of self-induced transparency of the Rayleigh wave is constructed. A thin resonance transition layer on an elastic surface is considered using a model of a two-dimensional gas of impurity paramagnetic atoms or quantum dots. Explicit analytical expressions for the profile and parameters of the Rayleigh vector soliton with two different oscillation frequencies is obtained, as well as simulations of this nonlinear surface acoustic wave with realistic parameters, which can be used in acoustic experiments. It is shown that the properties of a surface vector soliton of the Rayleigh wave depend on the parameters of the resonance layer, the elastic medium, and the transverse structure of the surface acoustic wave.

Figure 1

Plot of the ${\varepsilon }_{xx}$ (in arbitrary units) component of the deformation tensor at a fixed value of the $z$ coordinate showing the two-dimensional vector soliton of the Rayleigh wave and the transverse structure of the pulse when the resonant “forbidden” transition monolayer containing the ensemble of resonance paramagnetic atoms is present. Along the $x$ axis, the vector soliton amplitude decays exponentially as one moves away from the surface at $x=0$. At $x=0$, the profile of the vector soliton corresponds to the solution of Eq. (25).