We report on new types of two-component one-dimensional dark solitons (DSs) in a dual-core waveguide model with normal group-velocity dispersion and Kerr nonlinearity in both cores, the coupling between which is also dispersive. In the presence of the dispersive coupling, quiescent DSs supported by the zero-frequency background are always gray, being stable with the out-of-phase background, i.e...

For a typical NRZ pulse propagating in existing normally dispersive bers, we provide a uniform description of the optical transmission. There are three distinct regimes of the governing nonlinear Schrr odinger equation: the fully nonlinear dispersive regime (ND), which covers a small region of the pulse; and two limiting asymptotic regimes-nonlinear, weakly dispersive (ZD) (for the bulk of the ...

We show that a collection of two-level atoms in an optical cavity beyond the rotating wave approximation and in the dispersive-adiabatic and non-dispersive adiabatic regime constitutes a nonlinear medium and is capable of generating squeezed state of light. It is found that squeezing produced in the non-dispersive adiabatic regime is significantly high compared to that produced in the dispersiv...

The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, nondifferentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations f...

SnCl4/nano-sawdust was prepared as a carbohydrate-based catalyst containing of tin bearing cellulose units. The catalyst was characterized by X-ray diffraction (XRD), fourier transform infrared spectroscopy (FT-IR), field emission scanning electron microscopy (FESEM) and energy dispersive X-ray spectroscopy (EDS). The catalyst was applied successfully as a readily available, inexpensive, biodeg...

Ill posed linear and nonlinear initial value problems may be stabilized, that it converted to to well posed initial value problems, by the addition of purely nonscalar linear dispersive terms. This is a stability analog of the Turing instability. This idea applies to systems of quasilinear Schrödinger equations from nonlinear optics.

These notes were written as a guideline for a short talk; hence, the references and the statements of the theorems are often not given in full details. The point of these notes is to summarize the different directions that the study of dispersive equations has taken in the last ten years. I would like to mention here a few recent textbooks that treat different parts of this subject. They could ...

A new form of governing equations is derived from Hamilton’s principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws both for non-dispersive case (Lagrangian depends only on conserved quantities) and dispersive case (Lagrangian depends also on their derivatives). For non-di...

Transmit diversity through two-transmit and one-receive antennas (DISO) with Alamouti’s Space-Time block coding (STBC) assumes the channel be flat and static over the coding block. Lindskog and Paulraj have extended this scheme for a time dispersive channel by doing the space-time coding over a large data block such as one burst. This helps to achieve diversity gain on a time-dispersive channel...