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

Abstract

A theory of an acoustic vector soliton of the Love wave is constructed. The nonlinear Love wave propagating along the interface between of a plane surface layer and the elastic semi-space under the condition of acoustic self-induced transparency is investigated. A thin resonance transition layer containing paramagnetic impurity atoms or semiconductor quantum dots sandwiched between these two connected media. Explicit analytical expressions for the profile and parameters of the Love vector soliton are obtained. It is shown that the properties of the nonlinear Love wave depends on the parameters of the transition resonance layer, the connected elastic media and the transverse structure of the Love mode. Numerical investigations of the Love vector soliton is executed for the parameters of the layered structure ZnO/LiN bO3 and surface acoustic waves which can be reached in current experiments.

Two-component vector breather solution of the modified BBM equation

“…As a result, it was obtained that one of the main SIT pulse is not scalar 0π pulse, as was previously supposed, but the two-component vector 0π pulse of SIT, and the scalar 0π pulse is only some approximation [14][15][16][28][29][30][31][32][33][34][35]. Later, a similar two-component vector 0π pulse was obtained for acoustic nonlinear SIT waves [36][37][38][39][40]. Using the generalized PRM for studying nonresonant nonlinear waves in a dispersive and Kerr-type nonlinear susceptibility medium led to similar results -the formation of a two-component vector pulse OSDFW [41].…”

Two-component nonlinear wave of the Hirota equation

“…We have to note that the similar two-component nonlinear waves we met in the different fields of research for various nature of waves: optical, acoustic, magnetic, hydrodynamics and others [5,18,[24][25][26][27]. In the theory of the self-induced transparency such wave is called the vector 0π pulse [20][21][22].…”

Vector nonlinear wave of the NLS equation

“…We have to note that the two-component vector breathers can propagate also in the other physical systems [4,[14][15][16].…”

“…In order to consider the two-component vector breather solution of the Eq. ( 1), we use the generalized perturbative reduction method [3,4,[11][12][13][14][15][16] which makes it possible to transform the Born-Infeld equation for the functions ûl to the coupled nonlinear Schrödinger equations for auxiliary functions f (α) l,n . As a result, we obtain a two-component nonlinear pulse oscillating with the difference and sum of the frequencies and wave numbers.…”

“…For the reality of U , we set: û+1 = û * −1 . The purpose of the present work is to consider the two-component vector breather solution of the Born-Infeld equation (1) using the generalized perturbative reduction method [3,4,[11][12][13][14][15][16].…”