ABSTRACT
An approximate analytical solution of the non-integrable problem of steady-state adiabatic interaction of a cnoidal wave with a breather is obtained. The solving algorithm is described by the example of one-dimensional problem of steady-state interaction of a plane cnoidal wave with circular polarization (the "information" signal) with orthogonally polarized rational soliton (the "control" signal) in an isotropic nonlinear gyrotropic medium with Kerr nonlinearity and second-order group-velocity dispersion. It is shown that such the interaction results in a strong amplitude and frequency modulation of the information signal and this modulation is localized in the region where intensity of the control signal changes.
ABSTRACT
It is shown that cascade quasisynchronous frequency conversion due to quadratic nonlinearity can be described in terms of an effective cubic nonlinearity. This enables one to reduce a four-mode interaction problem to solving a system of two coupled nonlinear Schrödinger equations for the amplitudes of the waves participating in both nonlinear processes. Exact analytic solutions of the corresponding system are found in the form of multicomponent cnoidal waves with components expressed through a sum and a difference of two similar fundamental solutions of the Lamé equation with shifted arguments. It is shown that solutions obtained in such a way enable one to optimize the conversion efficiency because of full coverage of the range of possible boundary conditions.
ABSTRACT
It is shown that, in a three-coupled-mode approximation, exact analytical solution of a system of equations, that describes a steady-state parametric frequency conversion, can be obtained as a solution of three closed nonlinear Schrödinger equations, coupled only through their boundary conditions. A reason for such a possibility lies in the description of the competition of two simultaneous second-order nonlinear processes in terms of an effective cascade cubic nonlinearity. Specific features and nontrivial asymptotes of complex self-consistent periodic solutions of the nonlinear Schrödinger equation are discussed.
ABSTRACT
An algorithm of building up a different class of stable self-consistent multicomponent periodical solutions of the nonlinear Schrödinger equation--multicomponent cnoidal waves--has been formulated by the example of a nonlinear wave propagating through a photorefractive crystal with a drift nonlinear response. Exact analytical expressions, describing distribution of light field in the components, have been obtained for solutions, which include up to three mutually incoherent components. It has been shown that such cnoidal waves are stable and their spatial structure is robust to collisions with the same cnoidal waves and to stochastic perturbations of the components' intensity distributions in a sufficiently wide range of changing spatial period.
