A two-component phase-modulated soliton in a medium with a two-photon resonant transition

Two-component vector breather solution of the modified BBM equation

“…One component of such a vector pulse oscillating with the sum, and the second at the difference of frequencies and wavenumbers (OSDFW). 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].…”

“…For the study of the two-component nonlinear solitary wave solution of Eq. ( 1) we apply the generalized PRM [1,[14][15][16][28][29][30][31][32][33][34][35][36][37][38][39][40][41] by means of which we can transform Eq. (1) into the coupled NSEs.…”

“…Even though the generalized PRM was developed relatively recently, using this method, it was possible to establish a connection between a number of the nonlinear differential equations (or system of equations) with the coupled nonlinear Schrödinger equations (NSEs) and find solutions in the form of two-component vector breathers OSDFW. To these equations belong: the Sin-Gordon equation, the system of Maxwell-Bloch equations, the system of Maxwell-Liouville equations for the linearly and the circularly polarized pulses in an ensemble of semiconductor quantum dots, Maxwell wave equation in the dispersive Kerr-type medium, the system of Maxwell equation and the material equations for two-photon resonant transitions, the system of magnetic Bloch equations and the elastic wave equation, the modified Korteweg-de Vries equation or the modified Benjamin-Bona-Mahony (BBM) equation [1,[14][15][16][28][29][30][31][32][33][34][35][36][37][38][39][40][41].…”

Optical two-photon nonlinear waves in two-dimensional materials

“…is the Planck's constant, ω nm and µ nm are the frequencies and matrix elements of electric-dipole moments transitions between n and m level of energy of the impurity optical atoms or SQDs [2,3,19,22].…”