ABSTRACT
Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a PT-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the PT breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations.
ABSTRACT
We report the observation of a self-written waveguide inside a bulk methylene blue sensitized poly/vinyl alcohol)/acrylamide photopolymer material. Light from a low power He-Ne laser is focused into the material, and the evolution of the beam is monitored. The refractive index of the material is modulated in the region of high intensity due to photobleaching and photopolymerization effects occurring in the material. As a result, the beam propagates through the medium without any diffraction effects.
ABSTRACT
Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant,and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.
ABSTRACT
We consider an array of N Josephson junctions connected in parallel and explore the condition for chaotic synchronization. It is found that the outer junctions can be synchronized while they remain uncorrelated to the inner ones when an external biasing is applied. The stability of the solution is found out for the outer junctions in the synchronization manifold. Symmetry considerations lead to a situation wherein the inner junctions can synchronize for certain values of the parameter. In the presence of a phase difference between the applied fields, all the junctions exhibit phase synchronization. It is also found that chaotic motion changes to periodic in the presence of phase differences.
ABSTRACT
Propagation of an optical high-power cylindrically symmetric beam in a material characterized by cubic-quintic nonlinearity is studied both analytically and numerically. In this case we have to consider the self-defocusing effect caused by the presence of free electrons produced due to plasma formation. The variational method is used to study the system analytically. The finite-difference beam propagation method is used for the numerical analysis. Stable (2+1) D spatial solitons are observed. The analytical results are found to be in very good agreement with the numerical results.
ABSTRACT
Considering ultrashort pulse propagation in a nonlinear resonant fiber governed by Hirota-Maxwell Bloch equations, the soliton interaction in an erbium-doped fiber system associated with higher-order dispersion, self-steepening, and self-induced transparency effects is studied for the case when the fiber is driven with and without a constant pumping source. Using auto-Bäcklund-transformation, one- and two-soliton solutions are generated. The significance of the results is discussed in detail.
