New class of extremely short electromagnetic solitons

Integrable models of the dynamics of longitudinal-transverse acoustic pulses in a paramagnetic crystal

“…It can be easily shown that their collision results in shifts whose magnitude is the same as in the case of soliton and breather solutions of the RMB and SG equations. But the course of soliton interaction for the MSG equation depends essentially on the relation between the free soliton parameters and the equation coefficients, as was revealed in [35]. We plan to discuss the properties of breather solutions and the particuliarities of soliton collisions in the case of the MRMB and MSG equations in a separate publication.…”

“…These equations were investigated numerically and analytically respectively in [28] and [29], where it was shown that the character of the pulse-medium interaction depends essentially on the sign of the pulse polarity. In this case, these equations also determine the dynamics of quasilongitudinal sound in a deformed paramagnetic crystal with the effective spin S = 1 [30]. Furthermore, for q = 0 and d = 0, the MRMB equations become the two-component RMB equations describing the propagation of vector electromagnetic pulses in an optically uniaxial medium.…”

“…The presented analysis shows that the problem under consideration is characterized by asymmetry with respect to the polarity of the two acoustic field components: the component Ω 2 tends to decrease the quantum transition frequency, and the sign of the area of Ω 1 is determined by that of q. For an electromagnetic ESP in an anisotropic medium, this asymmetry was first revealed in [37] (for a detailed study of its manifestation in the MRMB system in some special cases, see [28]- [30] for d = 0 and [31] for q = 0).…”

“…It first appeared in [32] when considering the properties of Bäcklund transformations for the SG equation, and further studies of it followed the same direction [33]. It was recently shown that the MSG equation in the SO approximation describes the dynamics of a extremely short electromagnetic pulse in a system of nonsymmetric quantum objects of the type of quantum wells or wires [34], [35]. We note that for the propagation of an acoustic pulse to be describable using the MSG equation in our case, it must have a longitudinal-transverse structure.…”

“…We now proceed to consider a soliton solution of MSG equation (18) following [34] and [35]. We take the zero background, θ = 0, as the initial solution of the equation.…”