Biomedical subjects
Publications and source records attributed to K Hizanidis.
A novel method for obtaining analytical solitary wave solutions of the nonlinear Kronig-Penney model in periodic photonic structures with self-defocusing nonlinearity is applied for providing generic families of solutions corresponding to the gaps of the linear band structure. Characteristic cases are shown to be quite robust under propagation.
A modified canonical perturbation method is employed for analyzing the charged particle dynamics as they interact with localized waves with continuous spectrum. In contrast with periodic Hamiltonian models, where the method has already been applied in a multitude of respective systems, the system in hand is inherently aperiodic. The localized waves have the form of amplitude modulated electrostatic fields, ranging from ordinary wave packets to ultrashort pulses. The analytically obtained approximate invariants of the motion contain rich information for the structure of the phase space and the respective distribution functions.
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We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasielastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasielastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semiquantitative agreement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasielastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed transmission system.
The existence and stability of exact continuous-wave and dark-soliton solutions to a system consisting of the cubic complex Ginzburg-Landau (CGL) equation linearly coupled with a linear dissipative equation is studied. We demonstrate the existence of vast regions in the system's parameter space associated with stable dark-soliton solutions, having the form of the Nozaki-Bekki envelope holes, in contrast to the case of the conventional CGL equation, where they are unstable. In the case when the dark soliton is unstable, two different types of instability are identified. The proposed stabilized model may be realized in terms of a dual-core nonlinear optical fiber, with one core active and one passive.
We study the evolution of a solitary pulse in the cubic complex Ginzburg-Landau equation, including the third-order dispersion (TOD) as a small perturbation. We develop analytical approximations, which yield a TOD-induced velocity c of the pulse as a function of the ratio D of the second-order dispersion and filtering coefficients. The analytical predictions show agreement with the direct numerical simulations for two distinct intervals of D. A new feature of the pulse motion, which is a precursor of the transition to blowup, is presented: The pulse suddenly acquires a large acceleration in the reverse direction at D>D(cr) approximately -1.5 and without the reversal at D<D(cr). It is also demonstrated that the laminar-propagation distance L (before the onset of the ultimate turbulent stage) becomes maximum deep inside the normal-dispersion region, while TOD significantly increases L in the anomalous-dispersion region, where, otherwise, it is quite small. The model has a straightforward physical realization in terms of nonlinear optical fibers with losses and bandwidth-limited amplification (gain and filtering).
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Explore the source record for details and available documents.