Approximate solutions to a nonintegrable problem of propagation of elliptically polarised waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes

Adiabatic interaction between a dark soliton and a cnoidal wave with orthogonal circular polarizations in an isotropic gyrotropic nonlinear medium

“…Particular solutions to system (1) were found in [11,12] in the form of cnoidal waves (interacting during propagation), with equal periods of variation in their intensities. The approximate solutions to system (1) that were obtained in [13] showed also the possibility of existence of waves with significantly different periods of variation in |A ± | 2 . The adiabatic approach to analysis of system (1), developed in [21−24], is based on the selection of rapidly and slowly varying waves; this approach proved to be efficient in finding other approximate solutions to (1) [18−20].…”

“…It was shown that the role of the control signal is reduced in this case to rather strong amplitude and frequency modulation: changes in the instantaneous amplitude and frequency values for the information signal, which is localized in the region where the control signal intensity changes and the signal changes sign with a change in the sign of interaction constant σ 2 + σ 1 /2 in the propagation equations. The difference of the collision between a cnoidal wave and a dark soliton from the collision with a bright soliton [13] is that in the former case the fast-field component changes with a decrease in the nonlinear interaction component to zero, while in the latter case the corresponding change occurs when this nonlinear interaction enhances.…”

Adiabatic modulation of a cnoidal wave by a breather with orthogonal circular polarization in an isotropic gyrotropic nonlinear medium

“…Let's write a system of two coupled nonlinear Schrödinger equations (NSEs) for the problem of interaction of two plane light waves with orthogonal circular polarizations (the information and control signals) in a standard [20,21] To solve the system Eq. 1we firstly separate the variables in Eq.…”

“…Under certain restrictions this is a very promising approach. The most commonly used methods are the perturbation theory [19] and the linearization technique [20]. However, since breathers, solitons, and cnoidal waves are "purely nonlinear objects", they cannot be properly described in terms of lower-order perturbation theory [19] and require too long series of successive approximations.…”

“…However, since breathers, solitons, and cnoidal waves are "purely nonlinear objects", they cannot be properly described in terms of lower-order perturbation theory [19] and require too long series of successive approximations. Results obtained by the linearization technique must always be mentally extrapolated to the nonlinear case [20].…”