Collisions between spatiotemporal solitons of different dimensionality in a planar waveguide

Abstract

A (2+1)-dimensional nonlinear Schrödinger equation including third-order dispersion is a natural model of a waveguide, in which strong temporal dispersion is induced by a grating in order to make the existence of two-dimensional spatiotemporal solitons possible. By means of analytical and numerical methods, we demonstrate that this model may support, simultaneously, stable dark quasi-one-dimensional (stripe) solitons and two-dimensional elevation solitons ("antidark solitons") in the form of weakly localized "lumps." The spatial position of lumps can be controlled by passing stripe dark solitons through them in an arbitrary direction. To substantiate this mechanism, we analytically calculate a position shift generated by a headon collision between the stripe and lump. The obtained results are in good agreement with direct numerical simulations.

The reductive perturbation method and some of its applications

“…It can be reasonably conjectured that equation (154), which has also been derived from quasi-adiabatic following approximation [109], will still hold in the more general case of an arbitrary number of atomic levels, when the inverse of the characteristic pulse duration is much smaller than any of the transition frequencies of the atoms.…”

Lump solutions and interaction phenomena of the (3 + 1)-dimensional nonlinear evolution equations

“…Many studies have reported that lump solutions for some NLEEs restore their velocities, amplitudes and shapes after interacting with solitons, which show that interaction phenomenon are considered to be completely elastic (Fokas et al , 2001; Nistazakis et al , 2001). In contrast, there are some soliton equations that satisfy certain conditions such as collisions to become completely nonelastic interactions.…”

Probability of fade estimation for FSO links with time dispersion and turbulence modeled with the gamma–gamma or the I-K distribution

“…where T denotes the retarded time in ps, which is defined in the usual way as in many areas of optical communications and physics, as well, [38][39][40][41][42]. The norms |U(z,T)| 2 and |u(z,T)| 2 , stand for the expected and the instantaneous normalized and dimensionless intensities of the pulses arriving at the receiver.…”