Biomedical subjects
Publications and source records attributed to Mark J Ablowitz.
Incomplete collisions in wavelength-division-multiplexed return-to-zero transmission systems are analyzed by asymptotic methods. Formulas for frequency and timing shifts are obtained. The results agree with direct numerical calculations.
Dark and gray solitons in communication systems with strong dispersion management (DM) are obtained. These new modes are characterized by a decaying oscillatory background. Unlike the bright DM solitons in which the oscillations are observed only on a logarithmic scale, here the oscillations are dominant on a linear scale and become very strong for moderate map strength.
A vector discrete diffraction managed soliton system is introduced. The vector model describes propagation of two polarization modes interacting in a nonlinear waveguide array with varying diffraction via the cross-phase modulation coupling. In the limit of strong diffraction we derive averaged equations governing the slow dynamics of the beam's amplitudes, and their stationary (in the form of bright-bright vector bound state) and traveling wave solutions are found. Through an extensive series of direct numerical simulations, interactions between diffraction-managed solitons for different values of velocities, diffraction, and cross-phase modulation coefficient are studied. We compare each collision case with its classical counterpart (constant diffraction) and find that in both the scalar and vector diffraction management cases, the interaction picture involves beam shaping, fusion, fission, nearly elastic collisions, and, in some cases, multihump structures. The collision scenario is found, in both the scalar and vector diffraction managed cases, to be rather different from the classical case.
A method to find discrete solitons in nonlinear lattices is introduced. Using nonlinear optical waveguide arrays as a prototype application, both stationary and traveling-wave solitons are investigated. In the limit of small wave velocity, a fully discrete perturbative analysis yields formulas for the mode shapes and velocity.