Kink waves in an extended nonlinear Schrödinger equation with allowance for stimulated scattering and nonlinear dispersion
The stationary waves with nonlinear phase modulation in an extended nonlinear Schrödinger equation with nonlinear dispersion and stimulated Raman–scattering terms are considered. New class of a kink–waves are found. This waves exists as the result of balance of the stimulated Raman–scattering and nonlinear dispersion
The stationary waves with nonlinear phase modulation in the frame of the extended nonlinear Schrodinger equation with taking into account both the nonlinear dispersion and stimulated Raman-scattering terms are considered. Two classes of a kink–waves are found: one class exists as the result of balance of the stimulated Raman--scattering and nonlinear dispersion, other class – as the result of balance of the stimulated Raman-scattering and second-order linear dispersion. Is show that kink-waves with pedestal exist only in present of the nonlinear dispersion.
Dynamics of Langmuir solitons is considered in the framework of the extended nonlinear Schrödinger equation (NLSE), including a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, caused by stimulated scattering on damping ion-sound waves. Also included are spatially decreasing second-order dispersion (SOD) and increasing self-phase modulation (SPM), caused by spatial decreasing electron temperature of plasma. It is shown that the wavenumber downshift of solitons, caused by the pseudo-SRS, may be compensated by an upshift provided by the decreasing SOD and increasing SPM coefficients. An analytical solution for solitons is obtained in an approximate form. Analytical and numerical results agree well.
Dynamics of short solitons envelope in the frame of the third-order nonlinear Schrodinger equations taking into account stimulated Raman-scattering and inhomogeneous second– and third-order linear dispersion, nonlinear dispersion and cubic nonlinearity is considered. Compensation of the stimulated Raman-scattering effect by the increasing of the second-order linear dispersion is shown. In adiabatic approximation stable soliton’s propagation regime is found. Third-order linear dispersion and nonlinear dispersion inhomogeneity effect to stimulated Raman-scattering compensation is analyzed.
Generalized error-locating codes are discussed. An algorithm for calculation of the upper bound of the probability of erroneous decoding for known code parameters and the input error probability is given. Based on this algorithm, an algorithm for selection of the code parameters for a specified design and input and output error probabilities is constructed. The lower bound of the probability of erroneous decoding is given. Examples of the dependence of the probability of erroneous decoding on the input error probability are given and the behavior of the obtained curves is explained.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.