Acoustical vector solitons in anisotropic media

Abstract

The system of equations of self-induced transparency (SIT) for extraordinary wave in uniaxial anisotropic media by means of generalized reduction perturbation method are transformed to the coupled nonlinear Schrödinger equations. It is shown that in the theory of SIT the second derivatives have significant role and leads to the formation of a vector 0π pulse oscillating with the sum and difference of the frequencies. An explicit analytical expressions for the profile and parameters of the nonlinear wave are obtained. It is shown that along with scalar 2π pulse, the vector 0π pulse is also the basic pulse of SIT and the scalar 0π pulse of SIT is only an approximation which can be considered in some special cases. The conditions of the existence of the nonlinear extraordinary wave depends on the direction of propagation. The profile of the vector 0π pulse in anisotropic crystal of ruby is presented with characteristic parameters which usually met in experiments.

Vector soliton of self-induced transparency of a generalized love wave

“…The dispersion equation and the relations between quantities Ω ± and Q ± are given by Eqs. (17) and (19), respectively. The transverse profile of the Love-mode is given by Eq.…”

Two-Component Vector Breather

“…In this case, one component of such a vector pulse oscillates at the sum frequency and wavenumber and the second one oscillates at the difference frequency and wavenumber. This situation is realized for optical and acoustic resonant two-component vector breathers of self-induced transparency: vector 0π-pulses [3,4]. The study of nonresonant nonlinear waves in a dispersive and nonlinear Kerr-type medium led to similar results: the formation of a two-component vector breather oscillating at the sum and difference frequencies (SDFs) and wavenumbers [5].…”

“…In particular, the perturbative reduction method (PRM) is adapted for studying one-component solitary waves; in this case, one complex auxiliary function and two constant parameters are used [2]. In contrast to the PRM, its generalized version uses two complex auxiliary functions and eight constant parameters, which makes it possible to study two-component nonlinear solitary waves [3,4].…”

“…To study a two-component solution of Eq. ( 1), we use the generalized PRM [3][4][5], with the help of which function can be represented as (4) where and ε is a small parameter. This expansion makes it possible to separate in even more slowly varying auxiliary functions…”

“…≠ 0 and we obtain the equation (7) where (8) The solution of Eq. ( 5) is sought in the form (see, e.g., [3][4][5]) (9) where K ± , k ± , and ω ± are real constants and V 0 is the velocity of the nonlinear wave. We assume the inequalities (10) to be satisfied.…”