On stochastic dynamics of solitons in inhomogeneous optical fibers

An analytical treatment of the effect of axial inhomogeneity on femtosecond solitary waves near the zero dispersion point

“…It is evident that (19) expresses quantitatively the (qualitatively expected) fact that the solitary waves travel in the nonuniform fibers with velocities different than the corresponding ones in the ideal fibers. This actually means that the time it takes the (bright or dark) solitary wave to travel along a certain distance L in a inhomogeneous fiber is different, in general, from the corresponding one in an ideal fiber.…”

“…This actually means that the time it takes the (bright or dark) solitary wave to travel along a certain distance L in a inhomogeneous fiber is different, in general, from the corresponding one in an ideal fiber. Therefore, using (19), it is possible to calculate the corresponding time shift At, which is defined as At = l:A(dz/w) = s," dz(v;l -TI;') and is given by where the signs f corresponds to the bright (s = -1) and dark distance of about 25 km (Fig. 1).…”

Symplectic Runge--Kutta Semidiscretization for Stochastic Schrödinger Equation

“…Schrödinger equation, as one of the basic models for wave propagation, plays an essential role in various fields such as optics, quantum physics, optical fiber communications, plasma physics (see [24] and references therein). Recently, stochastic perturbations of this equation have been investigated ( [3,22,4,11]), where the perturbations may due to the inhomogeneous media or the thermal fluctuations, etc. More recently, some attentions have been paid to the studies of stochastic Schrödinger equation from both theoretical and numerical views; see [6,7,8,16,17].…”